Finite Group DatabasebetaFinite Group Databasebeta| order | 35706 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(D541⋊C3) |
| unambiguous semidirect product | (C541⋊C3)⋊D11 |
| unambiguous semidirect product | D5951⋊C3 |
| Fitting, socle, derived, Hall | C11×C541 ⋊ C2×C3 |
| Hall | C11×C541⋊C3 ⋊ C2 |
| Hall | D5951 ⋊ C3 |
| Hall | C541⋊C3 ⋊ D11 |
| Sylow | C541 ⋊ C3×D11 |
| Sylow | C11 ⋊ D541⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C541 | C2×C3 |
| LCS | G ▷ C11×C541 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 552 |
| transitive degree | μt(G) = 5951 |
A minimal faithful permutation representation — 2 generators on 552 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)(237,344,345,288,289,404)(239,342,343,291,287,336)(242,281,341,293,294,337)(249,357,358,300,301,332)(256,364,365,307,308,327)(262,371,372,314,315,322)(267,378,376,319,320,317)(272,383,369,324,325,311)(276,388,362,329,330,304)(279,393,355,333,334,297)(290,409,410,347,348,469)(292,407,408,350,346,401)(295,340,406,352,353,402)(302,421,422,359,360,397)(309,428,429,366,367,392)(316,433,434,373,374,387)(321,440,441,379,380,382)(326,446,438,384,385,377)(331,451,413,389,390,370)(335,456,426,394,395,363)(338,461,419,398,399,356)(349,457,458,412,396,508)(351,471,472,414,411,467)(354,405,470,416,417,468)(361,476,477,423,424,464)(368,481,482,430,431,460)(375,486,487,435,436,455)(381,491,492,442,443,450)(386,498,496,447,448,445)(391,503,474,452,453,439)(400,512,418,462,463,427)(403,514,475,465,466,420)(415,509,510,473,459,516)(425,517,518,478,479,515)(432,519,520,483,484,513)(437,523,524,488,489,511)(444,528,529,493,494,507)(449,533,522,499,500,502)(454,537,480,504,505,497)(485,538,539,521,506,543)(490,544,545,525,526,542)(495,546,547,530,531,541)(501,549,527,534,535,540)(532,550,551,548,536,552);(1,2,4,6,8,10,11,9,7,5,3)(12,13,16,22,30,43,62,85,114,149,190,237,290,349,413,369,310,257,206,158,108,58,77,93,78,57,76,103,135,172,214,262,316,375,437,490,527,529,487,429,358,284,186,229,269,264,259,252,245,230,185,228,279,335,396,459,479,484,489,494,500,505,510,410,470,514,512,508,503,498,491,486,481,476,471,409,462,398,294,189,234,248,255,261,266,271,275,278,280,336,397,460,511,541,548,530,493,442,379,319,265,217,174,118,61,82,95,99,102,104,136,173,215,263,317,377,439,473,414,350,291,238,191,150,115,86,63,44,31,15,19,24,34,48,67,90,119,154,195,242,295,354,418,426,362,303,250,203,162,123,79,39,54,55,38,53,74,100,131,167,209,256,309,368,432,485,522,492,434,365,299,231,145,182,216,211,205,198,183,144,181,226,276,331,391,454,506,526,531,535,539,518,472,345,406,461,456,451,446,440,433,428,421,407,344,405,465,353,236,287,301,308,315,320,325,330,334,337,339,401,464,513,542,552,550,534,499,447,384,324,270,221,153,84,111,125,130,134,137,139,177,220,268,322,382,445,497,478,423,359,300,247,200,159,124,94,69,47,21,27,35,49,68,92,121,156,197,244,297,356,420,475,419,355,296,243,196,155,120,91,56,26,37,25,36,51,71,96,126,161,202,249,302,361,425,480,496,441,372,306,246,184,110,141,169,164,157,142,109,140,179,223,272,326,386,449,501,536,551,545,520,477,408,286,341,393,388,383,378,371,364,357,342,285,340,403,417,289,346,360,367,374,380,385,390,395,399,402,404,467,515,543,549,546,544,538,504,452,389,329,274,194,113,146,160,166,171,175,178,180,224,273,327,387,450,502,521,483,430,366,307,254,207,165,129,98,66,29,40,50,52,72,97,127,163,204,251,304,363,427,416,352,293,240,193,152,117,88,65,46,33,18,17,23,32,45,64,87,116,151,192,239,292,351,415,474,438,376,313,253,199,143,81,106,128,122,107,80,105,138,176,219,267,321,381,444,495,532,547,524,482,422,343,233,282,328,323,318,312,305,298,283,232,281,338,400,348,411,424,431,436,443,448,453,458,463,466,468,469,516,537,533,528,523,519,517,509,457,394,333,241,148,187,201,208,213,218,222,225,227,277,332,392,455,507,540,525,488,435,373,314,260,212,170,133,89,42,59,70,73,75,101,132,168,210,258,311,370,412,347,288,235,188,147,112,83,60,41,28,20,14)Polycyclic presentation:
2,3,11,541|c^a=c^10,d^a=d^540,d^b=d^1291011 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35706, 12);