PΣL(2,𝔽₂₅) #72219556

order	15600
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₂

Aliases

projective special semilinear

PΣL(2,𝔽₂₅)

Splittings

socle, derived

PSL(2,𝔽₂₅) ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, cosocle, hypocenter	PSL(2,𝔽₂₅)	C₂
LCS	G ▷ PSL(2,𝔽₂₅)
UCS	C₁

103 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Permutation generators:

(1,561,566)(2,497,482)(3,283,298)(4,219,214)(5,210,560)(6,21,476)(7,557,292)(8,493,208)(9,279,24)(10,295,495)(11,206,286)(12,17,202)(13,553,18)(14,489,559)(15,480,280)(16,291,221)(19,574,494)(20,565,215)(22,287,572)(23,223,488)(25,305,320)(26,241,236)(28,588,593)(29,399,384)(30,390,230)(31,301,46)(32,237,587)(33,48,378)(34,584,319)(35,575,40)(36,386,581)(37,322,397)(38,233,313)(39,44,229)(41,596,391)(42,382,307)(43,318,248)(45,245,385)(47,592,242)(49,314,599)(50,610,615)(51,421,406)(52,332,347)(53,143,138)(55,70,400)(56,606,341)(57,417,132)(58,328,73)(59,139,614)(60,130,335)(61,66,126)(62,602,67)(63,413,608)(64,349,424)(65,340,145)(68,623,418)(69,409,334)(71,336,621)(72,147,412)(74,619,144)(75,165,160)(77,512,517)(78,448,433)(79,359,374)(80,350,95)(81,161,511)(82,97,427)(83,508,368)(84,444,159)(85,435,505)(86,371,446)(87,157,362)(88,93,153)(89,504,94)(90,520,440)(91,431,356)(92,367,172)(96,516,166)(98,363,523)(99,174,439)(100,470,455)(101,256,271)(102,192,187)(104,539,544)(105,530,265)(106,466,181)(107,252,122)(108,188,538)(109,124,454)(110,115,175)(111,526,116)(112,462,532)(113,273,473)(114,184,264)(117,547,467)(118,458,258)(119,269,199)(120,260,545)(121,196,461)(123,543,193)(127,622,607)(128,408,423)(129,344,339)(131,146,601)(133,618,333)(134,404,149)(135,420,620)(136,331,411)(137,142,327)(140,605,405)(141,416,346)(148,348,613)(150,430,445)(151,366,361)(154,524,509)(155,515,355)(156,426,171)(158,173,503)(162,447,522)(163,358,438)(164,169,354)(167,507,432)(168,443,373)(170,370,510)(176,546,531)(177,457,472)(178,268,263)(180,195,525)(182,542,257)(183,453,198)(185,255,460)(186,191,251)(189,474,549)(190,465,270)(194,534,459)(197,272,537)(200,290,285)(203,573,558)(204,484,499)(205,475,220)(207,222,552)(209,569,284)(211,496,571)(212,282,487)(213,218,278)(216,556,481)(217,492,297)(224,299,564)(225,595,580)(226,381,396)(227,317,312)(231,591,306)(232,377,247)(234,249,579)(235,240,300)(238,398,598)(239,309,389)(243,583,383)(244,394,324)(246,321,586)(253,533,548)(254,469,464)(259,529,274)(261,456,536)(262,267,452)(266,541,471)(275,555,570)(276,491,486)(281,551,296)(288,483,563)(289,294,479)(293,568,498)(302,582,597)(303,393,388)(308,578,323)(310,380,585)(311,316,376)(315,590,395)(325,415,410)(329,609,624)(330,600,345)(337,407,612)(338,343,403)(342,617,422)(351,506,521)(352,442,437)(357,502,372)(360,365,425)(364,434,514)(369,519,449)(379,594,589)(387,392,577)(401,616,611)(414,419,604)(428,518,513)(436,441,501)(450,540,535)(463,468,528)(477,567,562)(485,490,550);(1,591,586)(2,407,422)(3,373,358)(4,189,194)(5,585,185)(6,401,21)(7,367,582)(8,183,418)(9,24,354)(10,420,370)(11,361,181)(12,177,17)(13,18,578)(14,584,414)(15,355,405)(16,196,366)(19,419,599)(20,190,590)(22,597,362)(23,413,198)(25,430,445)(26,271,256)(27,212,217)(29,619,614)(30,265,605)(31,206,441)(32,47,252)(33,613,213)(34,429,49)(35,200,40)(36,41,601)(37,607,437)(38,448,273)(39,264,209)(42,442,622)(43,258,433)(44,224,269)(45,620,260)(46,436,221)(48,218,618)(50,235,240)(52,517,512)(53,458,473)(54,299,284)(55,70,275)(56,511,236)(57,452,72)(58,293,508)(59,234,469)(60,505,460)(61,471,296)(62,287,232)(63,228,68)(64,69,504)(65,465,520)(66,281,456)(67,247,292)(71,241,516)(73,523,288)(74,464,249)(75,540,535)(76,481,496)(77,322,307)(78,138,143)(80,475,95)(81,316,531)(82,132,492)(83,98,303)(84,539,139)(85,310,130)(86,126,91)(87,92,527)(88,533,488)(89,499,324)(90,145,315)(93,493,548)(94,309,484)(96,546,311)(97,487,147)(99,144,544)(100,345,330)(101,161,166)(103,568,563)(104,384,399)(105,155,390)(106,121,326)(107,562,162)(108,378,123)(109,344,559)(110,115,550)(111,556,386)(112,397,347)(113,338,158)(114,154,119)(116,391,571)(117,332,382)(118,173,343)(120,385,170)(122,167,567)(124,574,339)(127,532,547)(128,498,483)(129,314,319)(131,526,146)(133,308,543)(134,149,479)(135,545,495)(136,486,306)(137,302,142)(140,480,530)(141,321,491)(148,538,323)(150,555,570)(151,396,381)(152,337,342)(156,331,566)(157,172,377)(159,554,174)(160,325,165)(163,573,398)(164,389,334)(168,383,558)(169,349,394)(171,561,346)(175,360,365)(178,583,598)(179,424,409)(180,195,400)(182,577,197)(184,359,594)(186,596,421)(187,412,357)(188,353,193)(191,406,581)(192,372,417)(199,589,374)(201,606,621)(202,447,432)(203,263,268)(205,600,220)(207,257,617)(208,223,428)(210,435,255)(211,251,216)(214,624,449)(215,270,440)(219,434,609)(222,612,272)(225,470,455)(226,286,291)(229,509,524)(230,280,515)(231,246,451)(233,503,248)(237,522,472)(238,463,283)(239,279,244)(242,457,507)(243,298,468)(245,510,295)(253,623,608)(254,439,444)(259,274,604)(261,611,431)(262,427,267)(266,446,616)(276,521,506)(277,462,467)(282,297,502)(285,450,290)(289,514,459)(294,474,519)(300,485,490)(304,549,534)(305,320,525)(312,537,482)(313,478,318)(317,497,542)(327,572,557)(328,388,393)(333,348,553)(335,560,380)(336,376,341)(340,395,565)(350,595,580)(351,411,416)(356,371,576)(363,588,408)(364,404,369)(368,423,593)(379,564,569)(387,552,392)(402,587,592)(410,575,415)(425,610,615)(438,603,443)(453,513,518)(461,501,466)(476,536,541)(489,529,494);(1,566,500)(2,482,375)(3,298,250)(4,214,125)(5,94,215)(6,505,90)(7,446,590)(8,362,465)(9,153,340)(10,33,280)(11,599,155)(12,385,30)(13,301,530)(14,242,405)(15,122,495)(16,538,370)(17,454,245)(18,265,120)(19,181,620)(20,61,560)(21,602,435)(22,418,310)(23,334,185)(24,145,60)(25,73,320)(26,614,195)(27,400,70)(28,341,570)(29,132,445)(31,553,260)(32,494,135)(34,221,510)(35,76,575)(36,517,450)(37,433,325)(38,374,200)(39,160,75)(41,581,540)(42,397,415)(43,313,290)(44,229,165)(45,109,230)(46,545,105)(47,461,605)(48,252,480)(49,193,355)(50,116,615)(51,532,490)(52,473,365)(53,264,240)(54,175,115)(56,621,555)(57,412,430)(58,328,305)(59,144,180)(62,476,520)(63,292,395)(64,208,270)(65,88,335)(66,504,210)(67,440,85)(68,356,585)(69,172,460)(71,593,275)(72,384,150)(74,236,525)(77,391,535)(78,307,410)(79,248,285)(80,103,350)(81,544,225)(82,455,100)(83,271,600)(84,187,475)(86,608,315)(87,424,190)(89,126,565)(91,572,380)(92,488,255)(93,279,130)(96,511,595)(97,427,470)(98,368,345)(99,159,220)(101,523,330)(102,439,205)(104,166,580)(106,587,420)(107,378,295)(108,319,170)(111,526,610)(112,467,485)(113,258,360)(114,199,235)(117,406,550)(118,347,425)(119,138,300)(121,559,140)(123,286,515)(124,202,390)(127,481,589)(128,297,464)(129,213,339)(131,509,154)(133,361,529)(134,152,404)(136,598,369)(137,389,244)(139,241,619)(141,537,434)(142,453,309)(143,269,184)(146,601,524)(147,417,399)(148,333,274)(151,613,259)(156,552,474)(157,493,349)(158,284,224)(161,516,539)(162,432,414)(163,373,289)(167,396,604)(168,312,479)(169,228,354)(171,549,194)(173,251,569)(174,192,444)(176,531,554)(177,472,429)(178,263,304)(182,411,519)(183,327,394)(186,564,209)(188,291,584)(189,207,459)(191,503,299)(196,592,489)(197,383,364)(198,324,239)(201,579,249)(203,306,624)(204,247,499)(206,543,314)(211,607,379)(212,423,254)(216,571,594)(217,487,469)(218,278,344)(222,426,534)(223,367,409)(226,522,419)(227,438,294)(231,586,609)(232,377,484)(233,318,359)(237,466,574)(238,257,449)(243,346,514)(246,558,329)(253,296,548)(256,508,363)(261,597,428)(262,388,303)(266,536,518)(267,452,393)(272,416,583)(273,332,458)(276,612,468)(277,403,343)(281,551,533)(282,492,408)(287,431,623)(288,372,498)(293,311,563)(302,471,513)(308,326,578)(316,502,483)(317,443,358)(321,591,573)(322,382,448)(331,542,398)(336,606,588)(337,422,463)(342,486,528)(348,366,618)(351,521,603)(352,437,478)(357,376,568)(371,557,413)(381,507,447)(386,596,512)(392,451,577)(401,611,527)(407,491,617)(421,547,462)(436,562,477)(441,501,567)(456,541,582)(496,556,622);(5,20)(6,21)(7,22)(8,23)(9,24)(10,15)(11,16)(12,17)(13,18)(14,19)(30,45)(31,46)(32,47)(33,48)(34,49)(35,40)(36,41)(37,42)(38,43)(39,44)(55,70)(56,71)(57,72)(58,73)(59,74)(60,65)(61,66)(62,67)(63,68)(64,69)(80,95)(81,96)(82,97)(83,98)(84,99)(85,90)(86,91)(87,92)(88,93)(89,94)(105,120)(106,121)(107,122)(108,123)(109,124)(110,115)(111,116)(112,117)(113,118)(114,119)(130,145)(131,146)(132,147)(133,148)(134,149)(135,140)(136,141)(137,142)(138,143)(139,144)(155,170)(156,171)(157,172)(158,173)(159,174)(160,165)(161,166)(162,167)(163,168)(164,169)(180,195)(181,196)(182,197)(183,198)(184,199)(185,190)(186,191)(187,192)(188,193)(189,194)(205,220)(206,221)(207,222)(208,223)(209,224)(210,215)(211,216)(212,217)(213,218)(214,219)(230,245)(231,246)(232,247)(233,248)(234,249)(235,240)(236,241)(237,242)(238,243)(239,244)(255,270)(256,271)(257,272)(258,273)(259,274)(260,265)(261,266)(262,267)(263,268)(264,269)(280,295)(281,296)(282,297)(283,298)(284,299)(285,290)(286,291)(287,292)(288,293)(289,294)(305,320)(306,321)(307,322)(308,323)(309,324)(310,315)(311,316)(312,317)(313,318)(314,319)(330,345)(331,346)(332,347)(333,348)(334,349)(335,340)(336,341)(337,342)(338,343)(339,344)(355,370)(356,371)(357,372)(358,373)(359,374)(360,365)(361,366)(362,367)(363,368)(364,369)(380,395)(381,396)(382,397)(383,398)(384,399)(385,390)(386,391)(387,392)(388,393)(389,394)(405,420)(406,421)(407,422)(408,423)(409,424)(410,415)(411,416)(412,417)(413,418)(414,419)(430,445)(431,446)(432,447)(433,448)(434,449)(435,440)(436,441)(437,442)(438,443)(439,444)(455,470)(456,471)(457,472)(458,473)(459,474)(460,465)(461,466)(462,467)(463,468)(464,469)(480,495)(481,496)(482,497)(483,498)(484,499)(485,490)(486,491)(487,492)(488,493)(489,494)(505,520)(506,521)(507,522)(508,523)(509,524)(510,515)(511,516)(512,517)(513,518)(514,519)(530,545)(531,546)(532,547)(533,548)(534,549)(535,540)(536,541)(537,542)(538,543)(539,544)(555,570)(556,571)(557,572)(558,573)(559,574)(560,565)(561,566)(562,567)(563,568)(564,569)(580,595)(581,596)(582,597)(583,598)(584,599)(585,590)(586,591)(587,592)(588,593)(589,594)(605,620)(606,621)(607,622)(608,623)(609,624)(610,615)(611,616)(612,617)(613,618)(614,619)

Conjugacy classes & character table

18 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×PΣL(2,𝔽₂₅), PΓL(2,𝔽₂₅)
maximal normal subgroup of	C₂×PΣL(2,𝔽₂₅), PΓL(2,𝔽₂₅)
maximal quotient of	C₂×PΣL(2,𝔽₂₅), ΣL(2,𝔽₂₅)

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:

gap> G := Group((1,561,566)(2,497,482)(3,283,298)(4,219,214)(5,210,560)(6,21,476)(7,557,292)(8,493,208)(9,279,24)(10,295,495)(11,206,286)(12,17,202)(13,553,18)(14,489,559)(15,480,280)(16,291,221)(19,574,494)(20,565,215)(22,287,572)(23,223,488)(25,305,320)(26,241,236)(28,588,593)(29,399,384)(30,390,230)(31,301,46)(32,237,587)(33,48,378)(34,584,319)(35,575,40)(36,386,581)(37,322,397)(38,233,313)(39,44,229)(41,596,391)(42,382,307)(43,318,248)(45,245,385)(47,592,242)(49,314,599)(50,610,615)(51,421,406)(52,332,347)(53,143,138)(55,70,400)(56,606,341)(57,417,132)(58,328,73)(59,139,614)(60,130,335)(61,66,126)(62,602,67)(63,413,608)(64,349,424)(65,340,145)(68,623,418)(69,409,334)(71,336,621)(72,147,412)(74,619,144)(75,165,160)(77,512,517)(78,448,433)(79,359,374)(80,350,95)(81,161,511)(82,97,427)(83,508,368)(84,444,159)(85,435,505)(86,371,446)(87,157,362)(88,93,153)(89,504,94)(90,520,440)(91,431,356)(92,367,172)(96,516,166)(98,363,523)(99,174,439)(100,470,455)(101,256,271)(102,192,187)(104,539,544)(105,530,265)(106,466,181)(107,252,122)(108,188,538)(109,124,454)(110,115,175)(111,526,116)(112,462,532)(113,273,473)(114,184,264)(117,547,467)(118,458,258)(119,269,199)(120,260,545)(121,196,461)(123,543,193)(127,622,607)(128,408,423)(129,344,339)(131,146,601)(133,618,333)(134,404,149)(135,420,620)(136,331,411)(137,142,327)(140,605,405)(141,416,346)(148,348,613)(150,430,445)(151,366,361)(154,524,509)(155,515,355)(156,426,171)(158,173,503)(162,447,522)(163,358,438)(164,169,354)(167,507,432)(168,443,373)(170,370,510)(176,546,531)(177,457,472)(178,268,263)(180,195,525)(182,542,257)(183,453,198)(185,255,460)(186,191,251)(189,474,549)(190,465,270)(194,534,459)(197,272,537)(200,290,285)(203,573,558)(204,484,499)(205,475,220)(207,222,552)(209,569,284)(211,496,571)(212,282,487)(213,218,278)(216,556,481)(217,492,297)(224,299,564)(225,595,580)(226,381,396)(227,317,312)(231,591,306)(232,377,247)(234,249,579)(235,240,300)(238,398,598)(239,309,389)(243,583,383)(244,394,324)(246,321,586)(253,533,548)(254,469,464)(259,529,274)(261,456,536)(262,267,452)(266,541,471)(275,555,570)(276,491,486)(281,551,296)(288,483,563)(289,294,479)(293,568,498)(302,582,597)(303,393,388)(308,578,323)(310,380,585)(311,316,376)(315,590,395)(325,415,410)(329,609,624)(330,600,345)(337,407,612)(338,343,403)(342,617,422)(351,506,521)(352,442,437)(357,502,372)(360,365,425)(364,434,514)(369,519,449)(379,594,589)(387,392,577)(401,616,611)(414,419,604)(428,518,513)(436,441,501)(450,540,535)(463,468,528)(477,567,562)(485,490,550), (1,591,586)(2,407,422)(3,373,358)(4,189,194)(5,585,185)(6,401,21)(7,367,582)(8,183,418)(9,24,354)(10,420,370)(11,361,181)(12,177,17)(13,18,578)(14,584,414)(15,355,405)(16,196,366)(19,419,599)(20,190,590)(22,597,362)(23,413,198)(25,430,445)(26,271,256)(27,212,217)(29,619,614)(30,265,605)(31,206,441)(32,47,252)(33,613,213)(34,429,49)(35,200,40)(36,41,601)(37,607,437)(38,448,273)(39,264,209)(42,442,622)(43,258,433)(44,224,269)(45,620,260)(46,436,221)(48,218,618)(50,235,240)(52,517,512)(53,458,473)(54,299,284)(55,70,275)(56,511,236)(57,452,72)(58,293,508)(59,234,469)(60,505,460)(61,471,296)(62,287,232)(63,228,68)(64,69,504)(65,465,520)(66,281,456)(67,247,292)(71,241,516)(73,523,288)(74,464,249)(75,540,535)(76,481,496)(77,322,307)(78,138,143)(80,475,95)(81,316,531)(82,132,492)(83,98,303)(84,539,139)(85,310,130)(86,126,91)(87,92,527)(88,533,488)(89,499,324)(90,145,315)(93,493,548)(94,309,484)(96,546,311)(97,487,147)(99,144,544)(100,345,330)(101,161,166)(103,568,563)(104,384,399)(105,155,390)(106,121,326)(107,562,162)(108,378,123)(109,344,559)(110,115,550)(111,556,386)(112,397,347)(113,338,158)(114,154,119)(116,391,571)(117,332,382)(118,173,343)(120,385,170)(122,167,567)(124,574,339)(127,532,547)(128,498,483)(129,314,319)(131,526,146)(133,308,543)(134,149,479)(135,545,495)(136,486,306)(137,302,142)(140,480,530)(141,321,491)(148,538,323)(150,555,570)(151,396,381)(152,337,342)(156,331,566)(157,172,377)(159,554,174)(160,325,165)(163,573,398)(164,389,334)(168,383,558)(169,349,394)(171,561,346)(175,360,365)(178,583,598)(179,424,409)(180,195,400)(182,577,197)(184,359,594)(186,596,421)(187,412,357)(188,353,193)(191,406,581)(192,372,417)(199,589,374)(201,606,621)(202,447,432)(203,263,268)(205,600,220)(207,257,617)(208,223,428)(210,435,255)(211,251,216)(214,624,449)(215,270,440)(219,434,609)(222,612,272)(225,470,455)(226,286,291)(229,509,524)(230,280,515)(231,246,451)(233,503,248)(237,522,472)(238,463,283)(239,279,244)(242,457,507)(243,298,468)(245,510,295)(253,623,608)(254,439,444)(259,274,604)(261,611,431)(262,427,267)(266,446,616)(276,521,506)(277,462,467)(282,297,502)(285,450,290)(289,514,459)(294,474,519)(300,485,490)(304,549,534)(305,320,525)(312,537,482)(313,478,318)(317,497,542)(327,572,557)(328,388,393)(333,348,553)(335,560,380)(336,376,341)(340,395,565)(350,595,580)(351,411,416)(356,371,576)(363,588,408)(364,404,369)(368,423,593)(379,564,569)(387,552,392)(402,587,592)(410,575,415)(425,610,615)(438,603,443)(453,513,518)(461,501,466)(476,536,541)(489,529,494), (1,566,500)(2,482,375)(3,298,250)(4,214,125)(5,94,215)(6,505,90)(7,446,590)(8,362,465)(9,153,340)(10,33,280)(11,599,155)(12,385,30)(13,301,530)(14,242,405)(15,122,495)(16,538,370)(17,454,245)(18,265,120)(19,181,620)(20,61,560)(21,602,435)(22,418,310)(23,334,185)(24,145,60)(25,73,320)(26,614,195)(27,400,70)(28,341,570)(29,132,445)(31,553,260)(32,494,135)(34,221,510)(35,76,575)(36,517,450)(37,433,325)(38,374,200)(39,160,75)(41,581,540)(42,397,415)(43,313,290)(44,229,165)(45,109,230)(46,545,105)(47,461,605)(48,252,480)(49,193,355)(50,116,615)(51,532,490)(52,473,365)(53,264,240)(54,175,115)(56,621,555)(57,412,430)(58,328,305)(59,144,180)(62,476,520)(63,292,395)(64,208,270)(65,88,335)(66,504,210)(67,440,85)(68,356,585)(69,172,460)(71,593,275)(72,384,150)(74,236,525)(77,391,535)(78,307,410)(79,248,285)(80,103,350)(81,544,225)(82,455,100)(83,271,600)(84,187,475)(86,608,315)(87,424,190)(89,126,565)(91,572,380)(92,488,255)(93,279,130)(96,511,595)(97,427,470)(98,368,345)(99,159,220)(101,523,330)(102,439,205)(104,166,580)(106,587,420)(107,378,295)(108,319,170)(111,526,610)(112,467,485)(113,258,360)(114,199,235)(117,406,550)(118,347,425)(119,138,300)(121,559,140)(123,286,515)(124,202,390)(127,481,589)(128,297,464)(129,213,339)(131,509,154)(133,361,529)(134,152,404)(136,598,369)(137,389,244)(139,241,619)(141,537,434)(142,453,309)(143,269,184)(146,601,524)(147,417,399)(148,333,274)(151,613,259)(156,552,474)(157,493,349)(158,284,224)(161,516,539)(162,432,414)(163,373,289)(167,396,604)(168,312,479)(169,228,354)(171,549,194)(173,251,569)(174,192,444)(176,531,554)(177,472,429)(178,263,304)(182,411,519)(183,327,394)(186,564,209)(188,291,584)(189,207,459)(191,503,299)(196,592,489)(197,383,364)(198,324,239)(201,579,249)(203,306,624)(204,247,499)(206,543,314)(211,607,379)(212,423,254)(216,571,594)(217,487,469)(218,278,344)(222,426,534)(223,367,409)(226,522,419)(227,438,294)(231,586,609)(232,377,484)(233,318,359)(237,466,574)(238,257,449)(243,346,514)(246,558,329)(253,296,548)(256,508,363)(261,597,428)(262,388,303)(266,536,518)(267,452,393)(272,416,583)(273,332,458)(276,612,468)(277,403,343)(281,551,533)(282,492,408)(287,431,623)(288,372,498)(293,311,563)(302,471,513)(308,326,578)(316,502,483)(317,443,358)(321,591,573)(322,382,448)(331,542,398)(336,606,588)(337,422,463)(342,486,528)(348,366,618)(351,521,603)(352,437,478)(357,376,568)(371,557,413)(381,507,447)(386,596,512)(392,451,577)(401,611,527)(407,491,617)(421,547,462)(436,562,477)(441,501,567)(456,541,582)(496,556,622), (5,20)(6,21)(7,22)(8,23)(9,24)(10,15)(11,16)(12,17)(13,18)(14,19)(30,45)(31,46)(32,47)(33,48)(34,49)(35,40)(36,41)(37,42)(38,43)(39,44)(55,70)(56,71)(57,72)(58,73)(59,74)(60,65)(61,66)(62,67)(63,68)(64,69)(80,95)(81,96)(82,97)(83,98)(84,99)(85,90)(86,91)(87,92)(88,93)(89,94)(105,120)(106,121)(107,122)(108,123)(109,124)(110,115)(111,116)(112,117)(113,118)(114,119)(130,145)(131,146)(132,147)(133,148)(134,149)(135,140)(136,141)(137,142)(138,143)(139,144)(155,170)(156,171)(157,172)(158,173)(159,174)(160,165)(161,166)(162,167)(163,168)(164,169)(180,195)(181,196)(182,197)(183,198)(184,199)(185,190)(186,191)(187,192)(188,193)(189,194)(205,220)(206,221)(207,222)(208,223)(209,224)(210,215)(211,216)(212,217)(213,218)(214,219)(230,245)(231,246)(232,247)(233,248)(234,249)(235,240)(236,241)(237,242)(238,243)(239,244)(255,270)(256,271)(257,272)(258,273)(259,274)(260,265)(261,266)(262,267)(263,268)(264,269)(280,295)(281,296)(282,297)(283,298)(284,299)(285,290)(286,291)(287,292)(288,293)(289,294)(305,320)(306,321)(307,322)(308,323)(309,324)(310,315)(311,316)(312,317)(313,318)(314,319)(330,345)(331,346)(332,347)(333,348)(334,349)(335,340)(336,341)(337,342)(338,343)(339,344)(355,370)(356,371)(357,372)(358,373)(359,374)(360,365)(361,366)(362,367)(363,368)(364,369)(380,395)(381,396)(382,397)(383,398)(384,399)(385,390)(386,391)(387,392)(388,393)(389,394)(405,420)(406,421)(407,422)(408,423)(409,424)(410,415)(411,416)(412,417)(413,418)(414,419)(430,445)(431,446)(432,447)(433,448)(434,449)(435,440)(436,441)(437,442)(438,443)(439,444)(455,470)(456,471)(457,472)(458,473)(459,474)(460,465)(461,466)(462,467)(463,468)(464,469)(480,495)(481,496)(482,497)(483,498)(484,499)(485,490)(486,491)(487,492)(488,493)(489,494)(505,520)(506,521)(507,522)(508,523)(509,524)(510,515)(511,516)(512,517)(513,518)(514,519)(530,545)(531,546)(532,547)(533,548)(534,549)(535,540)(536,541)(537,542)(538,543)(539,544)(555,570)(556,571)(557,572)(558,573)(559,574)(560,565)(561,566)(562,567)(563,568)(564,569)(580,595)(581,596)(582,597)(583,598)(584,599)(585,590)(586,591)(587,592)(588,593)(589,594)(605,620)(606,621)(607,622)(608,623)(609,624)(610,615)(611,616)(612,617)(613,618)(614,619));

PΣL(2,𝔽25) #72219556

Aliases

Splittings

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

PΣL(2,𝔽₂₅) #72219556