C₁₁×C₄₂₁⋊C₅ #37529172

order	23155
automorphism	?
homology	Abelianization (H₁) = C₅×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×C₄₂₁⋊C₅
unambiguous semidirect product	C₄₂₁⋊(C₅×C₁₁)

Splittings

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

Subgroups

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23155, 2);

C11×C421⋊C5 #37529172