#37529175

order	23155
automorphism	?
homology	Abelianization (H₁) = C₅ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₁₁×C₄₂₁ ⋊ C₅
Sylow	C₄₂₁ ⋊ C₁₁⋊C₅
Sylow	C₁₁ ⋊ C₄₂₁⋊C₅

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁×C₄₂₁	C₅
LCS	G ▷ C₁₁×C₄₂₁
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 432
transitive degree	μ_t(G) = 4631

A minimal faithful permutation representation — 2 generators on 432 points:

(2,3,5,9,17)(4,7,13,25,48)(6,11,21,40,33)(8,15,29,51,93)(10,19,36,18,34)(12,23,44,81,89)(14,27,52,95,63)(16,31,59,107,179)(20,38,70,49,90)(22,42,77,74,64)(24,46,85,146,157)(26,50,91,35,65)(28,54,99,165,153)(30,57,103,168,113)(32,61,55,101,169)(37,68,41,75,67)(39,72,125,94,158)(43,79,136,140,154)(45,83,142,159,114)(47,87,149,233,268)(53,97,161,129,115)(56,98,163,66,116)(58,105,175,262,237)(60,109,182,272,187)(62,111,145,227,314)(69,120,82,141,155)(71,123,96,160,118)(73,127,203,180,269)(76,131,122,92,156)(78,134,133,130,119)(80,138,218,229,241)(84,144,225,248,238)(86,112,185,252,188)(88,151,199,288,253)(100,167,250,242,189)(102,171,256,192,281)(104,174,260,207,190)(106,177,172,258,110)(108,181,270,117,191)(121,196,147,230,246)(124,198,166,249,239)(126,201,173,255,193)(128,205,278,170,254)(132,210,200,164,247)(135,213,215,222,240)(137,216,223,243,194)(139,220,309,323,350)(143,224,244,208,195)(148,231,319,343,326)(150,234,324,352,277)(152,236,305,375,380)(162,245,212,209,197)(176,264,345,329,279)(178,266,317,368,358)(183,274,354,296,280)(184,232,321,386,339)(186,276,341,297,286)(202,290,263,344,327)(204,293,273,353,283)(206,295,361,315,381)(211,300,292,271,351)(214,303,306,318,332)(217,304,312,333,328)(219,307,275,337,284)(221,311,369,363,336)(226,313,334,330,285)(228,316,382,282,359)(235,291,365,259,340)(251,335,331,298,287)(257,338,301,372,356)(261,342,302,299,289)(265,267,348,294,357)(308,376,384,395,391)(310,378,390,400,360)(320,385,396,392,362)(322,388,416,407,403)(325,377,412,414,394)(346,397,393,370,364)(347,389,411,409,402)(349,399,379,408,406)(355,401,374,371,366)(367,405,387,415,398)(373,410,404,383,413)(417,421,420,419,418)(423,424,426,429,432)(425,428,427,430,431);(1,2,4,8,16,32,62,112,186,274,355,203,292,319,384,375,23,45,84,145,228,317,141,222,191,280,161,244,331,393,167,251,171,257,218,306,324,390,351,38,71,124,199,68,119,194,284,360,399,165,248,57,104,174,261,220,310,225,312,288,363,353,400,410,419,256,75,130,208,297,91,155,239,327,83,143,181,271,125,200,185,275,303,7,14,28,55,102,172,259,321,387,397,95,159,242,329,97,162,87,150,136,215,233,323,269,350,359,403,149,34,64,114,188,277,340,394,376,27,53,98,164,127,204,142,223,196,286,362,405,418,421,169,253,177,265,342,48,89,153,237,42,78,135,214,70,122,146,229,210,299,370,408,59,108,175,263,227,315,344,395,290,364,354,50,92,31,60,77,133,212,302,374,411,420,413,85,147,182,273,247,332,236,325,304,11,22,43,80,139,221,81,140,116,190,279,357,402,415,99,166,101,170,255,337,295,367,270,19,37,69,121,36,67,118,193,283,348,398,378,29,56,103,173,138,219,308,377,198,287,272,352,372,409,335,40,74,129,207,296,368,407,381,44,82,107,180,158,241,111,184,213,3,6,12,24,47,88,152,231,320,345,396,293,366,385,52,96,46,86,148,232,322,389,179,268,281,358,245,17,33,63,113,187,258,339,307,13,26,51,94,72,126,202,291,120,195,285,361,404,416,249,333,105,176,260,341,311,379,313,21,41,76,132,211,301,373,338,131,209,298,369,156,240,328,391,144,226,262,343,201,289,276,25,49,15,30,58,106,178,267,349,388,417,382,160,243,330,392,163,246,151,235,216,5,10,20,39,73,128,206,234,65,115,189,278,356,386,414,412,54,100,168,252,205,294,224,9,18,35,66,117,192,282,254,336,266,347,309,90,154,238,326,79,137,217,305,123,197,230,318,300,371,250,334,109,183,264,346,316,383,314,380,365,406,401,93,157,61,110,134)(422,423,425,426,429,424,427,431,430,432,428)

Polycyclic presentation:

5,11,421|b^a=b^5,c^a=c^252

Conjugacy classes & character table

931 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23155, 5);