Finite Group DatabasebetaFinite Group Databasebeta| order | 32142 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(D487⋊C3) |
| unambiguous semidirect product | (C487⋊C3)⋊D11 |
| unambiguous semidirect product | D5357⋊C3 |
| Fitting, socle, derived, Hall | C11×C487 ⋊ C2×C3 |
| Hall | C11×C487⋊C3 ⋊ C2 |
| Hall | D5357 ⋊ C3 |
| Hall | C487⋊C3 ⋊ D11 |
| Sylow | C487 ⋊ C3×D11 |
| Sylow | C11 ⋊ D487⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C487 | C2×C3 |
| LCS | G ▷ C11×C487 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 498 |
| transitive degree | μt(G) = 5357 |
A minimal faithful permutation representation — 2 generators on 498 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(13,17,18,14,15,19)(16,25,26,20,21,35)(22,38,39,28,29,52)(23,37,33,31,27,24)(30,57,58,41,42,75)(32,55,56,44,40,49)(34,36,54,46,47,50)(43,80,81,60,61,104)(45,78,79,63,59,72)(48,53,77,65,66,73)(51,93,91,69,70,68)(62,109,110,83,84,139)(64,107,108,86,82,101)(67,76,106,88,89,102)(71,122,123,94,95,97)(74,128,120,98,99,92)(85,144,145,112,113,180)(87,142,143,115,111,136)(90,105,141,117,118,137)(96,157,158,124,125,132)(100,164,162,129,130,127)(103,169,155,133,134,121)(114,185,186,147,148,227)(116,183,184,150,146,177)(119,140,182,152,153,178)(126,198,199,159,160,173)(131,205,206,165,166,168)(135,211,203,170,171,163)(138,216,196,174,175,156)(149,232,233,188,189,280)(151,230,231,191,187,224)(154,181,229,193,194,225)(161,245,246,200,201,220)(167,252,253,207,208,215)(172,259,257,212,213,210)(176,264,250,217,218,204)(179,269,243,221,222,197)(190,285,286,235,236,339)(192,283,284,238,234,277)(195,228,282,240,241,278)(202,298,299,247,248,273)(209,305,306,254,255,268)(214,312,313,260,261,263)(219,318,310,265,266,258)(223,323,303,270,271,251)(226,328,296,274,275,244)(237,344,345,288,289,399)(239,342,343,291,287,336)(242,281,341,293,294,337)(249,353,354,300,301,332)(256,360,361,307,308,327)(262,367,368,314,315,322)(267,374,372,319,320,317)(272,379,365,324,325,311)(276,384,358,329,330,304)(279,389,348,333,334,297)(290,394,395,347,338,445)(292,401,402,349,346,397)(295,340,400,351,352,398)(302,405,406,355,356,393)(309,410,411,362,363,388)(316,417,418,369,370,383)(321,424,425,375,376,378)(326,430,422,380,381,373)(331,435,415,385,386,366)(335,440,404,390,391,359)(350,446,447,403,396,449)(357,450,451,407,408,448)(364,452,453,412,413,444)(371,456,457,419,420,439)(377,461,462,426,427,434)(382,468,466,431,432,429)(387,473,455,436,437,423)(392,478,409,441,442,416)(414,479,480,454,443,482)(421,483,484,458,459,481)(428,485,486,463,464,477)(433,489,488,469,470,472)(438,493,460,474,475,467)(465,494,495,487,476,497)(471,498,492,490,491,496);(1,2,4,6,8,10,11,9,7,5,3)(12,13,16,22,30,43,62,85,114,149,190,237,290,348,296,243,196,155,120,91,56,26,37,25,36,51,71,96,126,161,202,249,302,357,409,415,365,310,257,206,158,108,58,77,93,78,57,76,103,135,172,214,262,316,371,421,460,466,425,368,306,246,184,110,141,169,164,157,142,109,140,179,223,272,326,382,433,471,492,486,457,411,354,284,186,229,269,264,259,252,245,230,185,228,279,335,392,443,459,464,470,475,480,451,402,286,341,389,384,379,374,367,360,353,342,285,340,289,346,356,363,370,376,381,386,391,395,398,399,449,478,473,468,461,456,452,450,446,394,294,189,234,248,255,261,266,271,275,278,280,336,393,444,481,497,498,494,474,436,385,329,274,194,113,146,160,166,171,175,178,180,224,273,327,383,434,472,487,463,426,375,319,265,217,174,118,61,82,95,99,102,104,136,173,215,263,317,373,423,454,412,362,307,254,207,165,129,98,66,29,40,50,52,72,97,127,163,204,251,304,359,403,349,291,238,191,150,115,86,63,44,31,15,19,24,34,48,67,90,119,154,195,242,295,351,293,240,193,152,117,88,65,46,33,18,17,23,32,45,64,87,116,151,192,239,292,350,404,358,303,250,203,162,123,79,39,54,55,38,53,74,100,131,167,209,256,309,364,414,455,422,372,313,253,199,143,81,106,128,122,107,80,105,138,176,219,267,321,377,428,465,488,462,418,361,299,231,145,182,216,211,205,198,183,144,181,226,276,331,387,438,476,491,495,484,453,406,343,233,282,328,323,318,312,305,298,283,232,281,338,396,408,413,420,427,432,437,442,447,345,400,445,440,435,430,424,417,410,405,401,344,352,236,287,301,308,315,320,325,330,334,337,339,397,448,482,493,489,485,483,479,441,390,333,241,148,187,201,208,213,218,222,225,227,277,332,388,439,477,496,490,469,431,380,324,270,221,153,84,111,125,130,134,137,139,177,220,268,322,378,429,467,458,419,369,314,260,212,170,133,89,42,59,70,73,75,101,132,168,210,258,311,366,416,407,355,300,247,200,159,124,94,69,47,21,27,35,49,68,92,121,156,197,244,297,347,288,235,188,147,112,83,60,41,28,20,14)Polycyclic presentation:
2,3,11,487|c^a=c^10,d^a=d^486,d^b=d^232912 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32142, 12);