C₂×D₁₄₉₇₇ #72295307

order	59908
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₂₉₉₅₄
direct product	C₂×D₁₄₉₇₇

Splittings

Fitting, socle	C₂×C₁₇×C₈₈₁ ⋊ C₂
derived, Hall	C₁₇×C₈₈₁ ⋊ C₂²
Sylow	C₈₈₁ ⋊ C₂×D₁₇
Sylow	C₁₇ ⋊ C₂×D₈₈₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₁₄₉₇₇
commutator, cosocle, hypocenter	C₁₇×C₈₈₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₁₇×C₈₈₁	C₂
LCS	G ▷ C₁₇×C₈₈₁
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 900
transitive degree	μ_t(G) = 29954

A minimal faithful permutation representation — 2 generators on 900 points:

(1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900);(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)(21,900)(22,899)(23,898)(24,897)(25,896)(26,895)(27,894)(28,893)(29,892)(30,891)(31,890)(32,889)(33,888)(34,887)(35,886)(36,885)(37,884)(38,883)(39,882)(40,881)(41,880)(42,879)(43,878)(44,877)(45,876)(46,875)(47,874)(48,873)(49,872)(50,871)(51,870)(52,869)(53,868)(54,867)(55,866)(56,865)(57,864)(58,863)(59,862)(60,861)(61,860)(62,859)(63,858)(64,857)(65,856)(66,855)(67,854)(68,853)(69,852)(70,851)(71,850)(72,849)(73,848)(74,847)(75,846)(76,845)(77,844)(78,843)(79,842)(80,841)(81,840)(82,839)(83,838)(84,837)(85,836)(86,835)(87,834)(88,833)(89,832)(90,831)(91,830)(92,829)(93,828)(94,827)(95,826)(96,825)(97,824)(98,823)(99,822)(100,821)(101,820)(102,819)(103,818)(104,817)(105,816)(106,815)(107,814)(108,813)(109,812)(110,811)(111,810)(112,809)(113,808)(114,807)(115,806)(116,805)(117,804)(118,803)(119,802)(120,801)(121,800)(122,799)(123,798)(124,797)(125,796)(126,795)(127,794)(128,793)(129,792)(130,791)(131,790)(132,789)(133,788)(134,787)(135,786)(136,785)(137,784)(138,783)(139,782)(140,781)(141,780)(142,779)(143,778)(144,777)(145,776)(146,775)(147,774)(148,773)(149,772)(150,771)(151,770)(152,769)(153,768)(154,767)(155,766)(156,765)(157,764)(158,763)(159,762)(160,761)(161,760)(162,759)(163,758)(164,757)(165,756)(166,755)(167,754)(168,753)(169,752)(170,751)(171,750)(172,749)(173,748)(174,747)(175,746)(176,745)(177,744)(178,743)(179,742)(180,741)(181,740)(182,739)(183,738)(184,737)(185,736)(186,735)(187,734)(188,733)(189,732)(190,731)(191,730)(192,729)(193,728)(194,727)(195,726)(196,725)(197,724)(198,723)(199,722)(200,721)(201,720)(202,719)(203,718)(204,717)(205,716)(206,715)(207,714)(208,713)(209,712)(210,711)(211,710)(212,709)(213,708)(214,707)(215,706)(216,705)(217,704)(218,703)(219,702)(220,701)(221,700)(222,699)(223,698)(224,697)(225,696)(226,695)(227,694)(228,693)(229,692)(230,691)(231,690)(232,689)(233,688)(234,687)(235,686)(236,685)(237,684)(238,683)(239,682)(240,681)(241,680)(242,679)(243,678)(244,677)(245,676)(246,675)(247,674)(248,673)(249,672)(250,671)(251,670)(252,669)(253,668)(254,667)(255,666)(256,665)(257,664)(258,663)(259,662)(260,661)(261,660)(262,659)(263,658)(264,657)(265,656)(266,655)(267,654)(268,653)(269,652)(270,651)(271,650)(272,649)(273,648)(274,647)(275,646)(276,645)(277,644)(278,643)(279,642)(280,641)(281,640)(282,639)(283,638)(284,637)(285,636)(286,635)(287,634)(288,633)(289,632)(290,631)(291,630)(292,629)(293,628)(294,627)(295,626)(296,625)(297,624)(298,623)(299,622)(300,621)(301,620)(302,619)(303,618)(304,617)(305,616)(306,615)(307,614)(308,613)(309,612)(310,611)(311,610)(312,609)(313,608)(314,607)(315,606)(316,605)(317,604)(318,603)(319,602)(320,601)(321,600)(322,599)(323,598)(324,597)(325,596)(326,595)(327,594)(328,593)(329,592)(330,591)(331,590)(332,589)(333,588)(334,587)(335,586)(336,585)(337,584)(338,583)(339,582)(340,581)(341,580)(342,579)(343,578)(344,577)(345,576)(346,575)(347,574)(348,573)(349,572)(350,571)(351,570)(352,569)(353,568)(354,567)(355,566)(356,565)(357,564)(358,563)(359,562)(360,561)(361,560)(362,559)(363,558)(364,557)(365,556)(366,555)(367,554)(368,553)(369,552)(370,551)(371,550)(372,549)(373,548)(374,547)(375,546)(376,545)(377,544)(378,543)(379,542)(380,541)(381,540)(382,539)(383,538)(384,537)(385,536)(386,535)(387,534)(388,533)(389,532)(390,531)(391,530)(392,529)(393,528)(394,527)(395,526)(396,525)(397,524)(398,523)(399,522)(400,521)(401,520)(402,519)(403,518)(404,517)(405,516)(406,515)(407,514)(408,513)(409,512)(410,511)(411,510)(412,509)(413,508)(414,507)(415,506)(416,505)(417,504)(418,503)(419,502)(420,501)(421,500)(422,499)(423,498)(424,497)(425,496)(426,495)(427,494)(428,493)(429,492)(430,491)(431,490)(432,489)(433,488)(434,487)(435,486)(436,485)(437,484)(438,483)(439,482)(440,481)(441,480)(442,479)(443,478)(444,477)(445,476)(446,475)(447,474)(448,473)(449,472)(450,471)(451,470)(452,469)(453,468)(454,467)(455,466)(456,465)(457,464)(458,463)(459,462)(460,461)

Conjugacy classes & character table

14980 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900), (4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)(21,900)(22,899)(23,898)(24,897)(25,896)(26,895)(27,894)(28,893)(29,892)(30,891)(31,890)(32,889)(33,888)(34,887)(35,886)(36,885)(37,884)(38,883)(39,882)(40,881)(41,880)(42,879)(43,878)(44,877)(45,876)(46,875)(47,874)(48,873)(49,872)(50,871)(51,870)(52,869)(53,868)(54,867)(55,866)(56,865)(57,864)(58,863)(59,862)(60,861)(61,860)(62,859)(63,858)(64,857)(65,856)(66,855)(67,854)(68,853)(69,852)(70,851)(71,850)(72,849)(73,848)(74,847)(75,846)(76,845)(77,844)(78,843)(79,842)(80,841)(81,840)(82,839)(83,838)(84,837)(85,836)(86,835)(87,834)(88,833)(89,832)(90,831)(91,830)(92,829)(93,828)(94,827)(95,826)(96,825)(97,824)(98,823)(99,822)(100,821)(101,820)(102,819)(103,818)(104,817)(105,816)(106,815)(107,814)(108,813)(109,812)(110,811)(111,810)(112,809)(113,808)(114,807)(115,806)(116,805)(117,804)(118,803)(119,802)(120,801)(121,800)(122,799)(123,798)(124,797)(125,796)(126,795)(127,794)(128,793)(129,792)(130,791)(131,790)(132,789)(133,788)(134,787)(135,786)(136,785)(137,784)(138,783)(139,782)(140,781)(141,780)(142,779)(143,778)(144,777)(145,776)(146,775)(147,774)(148,773)(149,772)(150,771)(151,770)(152,769)(153,768)(154,767)(155,766)(156,765)(157,764)(158,763)(159,762)(160,761)(161,760)(162,759)(163,758)(164,757)(165,756)(166,755)(167,754)(168,753)(169,752)(170,751)(171,750)(172,749)(173,748)(174,747)(175,746)(176,745)(177,744)(178,743)(179,742)(180,741)(181,740)(182,739)(183,738)(184,737)(185,736)(186,735)(187,734)(188,733)(189,732)(190,731)(191,730)(192,729)(193,728)(194,727)(195,726)(196,725)(197,724)(198,723)(199,722)(200,721)(201,720)(202,719)(203,718)(204,717)(205,716)(206,715)(207,714)(208,713)(209,712)(210,711)(211,710)(212,709)(213,708)(214,707)(215,706)(216,705)(217,704)(218,703)(219,702)(220,701)(221,700)(222,699)(223,698)(224,697)(225,696)(226,695)(227,694)(228,693)(229,692)(230,691)(231,690)(232,689)(233,688)(234,687)(235,686)(236,685)(237,684)(238,683)(239,682)(240,681)(241,680)(242,679)(243,678)(244,677)(245,676)(246,675)(247,674)(248,673)(249,672)(250,671)(251,670)(252,669)(253,668)(254,667)(255,666)(256,665)(257,664)(258,663)(259,662)(260,661)(261,660)(262,659)(263,658)(264,657)(265,656)(266,655)(267,654)(268,653)(269,652)(270,651)(271,650)(272,649)(273,648)(274,647)(275,646)(276,645)(277,644)(278,643)(279,642)(280,641)(281,640)(282,639)(283,638)(284,637)(285,636)(286,635)(287,634)(288,633)(289,632)(290,631)(291,630)(292,629)(293,628)(294,627)(295,626)(296,625)(297,624)(298,623)(299,622)(300,621)(301,620)(302,619)(303,618)(304,617)(305,616)(306,615)(307,614)(308,613)(309,612)(310,611)(311,610)(312,609)(313,608)(314,607)(315,606)(316,605)(317,604)(318,603)(319,602)(320,601)(321,600)(322,599)(323,598)(324,597)(325,596)(326,595)(327,594)(328,593)(329,592)(330,591)(331,590)(332,589)(333,588)(334,587)(335,586)(336,585)(337,584)(338,583)(339,582)(340,581)(341,580)(342,579)(343,578)(344,577)(345,576)(346,575)(347,574)(348,573)(349,572)(350,571)(351,570)(352,569)(353,568)(354,567)(355,566)(356,565)(357,564)(358,563)(359,562)(360,561)(361,560)(362,559)(363,558)(364,557)(365,556)(366,555)(367,554)(368,553)(369,552)(370,551)(371,550)(372,549)(373,548)(374,547)(375,546)(376,545)(377,544)(378,543)(379,542)(380,541)(381,540)(382,539)(383,538)(384,537)(385,536)(386,535)(387,534)(388,533)(389,532)(390,531)(391,530)(392,529)(393,528)(394,527)(395,526)(396,525)(397,524)(398,523)(399,522)(400,521)(401,520)(402,519)(403,518)(404,517)(405,516)(406,515)(407,514)(408,513)(409,512)(410,511)(411,510)(412,509)(413,508)(414,507)(415,506)(416,505)(417,504)(418,503)(419,502)(420,501)(421,500)(422,499)(423,498)(424,497)(425,496)(426,495)(427,494)(428,493)(429,492)(430,491)(431,490)(432,489)(433,488)(434,487)(435,486)(436,485)(437,484)(438,483)(439,482)(440,481)(441,480)(442,479)(443,478)(444,477)(445,476)(446,475)(447,474)(448,473)(449,472)(450,471)(451,470)(452,469)(453,468)(454,467)(455,466)(456,465)(457,464)(458,463)(459,462)(460,461));

C2×D14977 #72295307