Finite Group DatabasebetaFinite Group Databasebeta| order | 12964 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic463⋊C7 |
| unambiguous semidirect product | (C463⋊C7)⋊C4 |
| derived, Sylow | C463 ⋊ C4×C7 |
| Hall | C463⋊C7 ⋊ C4 |
| Hall | Dic463 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D463⋊C7 |
| commutator, hypocenter | C463 | C4×C7 |
| Fitting, socle, cosocle | C2×C463 | C2×C7 |
| prime radical | C2×C463⋊C7 | C2 |
| LCS | G ▷ C463 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 467 |
| transitive degree | μt(G) = 1852 |
A minimal faithful permutation representation — 2 generators on 467 points:
(2,6,7,25,30,106,121,3,4,12,14,52,62,177)(5,19,20,11,46,47,36,9,10,40,22,23,94,73)(8,35,29,116,117,48,176,16,17,59,60,206,97,98)(13,56,57,200,203,383,404,27,28,111,113,321,310,287)(15,66,67,222,224,214,174,32,33,127,128,339,122,96)(18,75,76,242,244,249,74,37,38,141,143,371,146,139)(21,88,89,130,269,357,286,43,44,68,163,228,348,208)(24,100,101,105,245,306,275,49,50,181,183,191,374,394)(26,108,109,311,314,192,406,54,55,195,197,416,307,289)(31,124,125,340,63,173,164,64,65,217,219,95,123,90)(34,132,133,361,362,281,77,69,70,231,232,444,172,145)(39,147,148,320,363,408,81,78,79,250,251,308,295,152)(41,154,71,204,236,298,299,82,83,135,136,325,187,405)(42,61,158,211,229,337,338,85,86,119,264,332,215,216)(45,166,167,180,393,261,140,91,92,259,273,290,155,240)(51,188,189,241,178,179,58,103,104,300,302,99,288,115)(53,138,156,267,193,194,407,72,84,239,161,107,309,297)(80,255,256,260,144,190,375,150,151,380,376,246,247,304)(87,157,266,285,207,396,149,159,160,263,386,328,282,253)(93,276,277,257,284,202,153,169,170,395,382,175,112,258)(102,296,142,199,372,278,327,185,186,110,243,319,397,248)(114,134,326,365,463,389,294,162,205,234,424,432,415,184)(118,329,330,334,126,293,347,209,210,212,343,182,221,331)(120,323,335,291,445,402,168,201,213,428,409,410,283,274)(129,354,355,351,352,344,345,226,227,356,225,358,220,333)(131,313,359,458,373,379,165,196,230,419,413,324,254,271)(137,336,369,420,459,455,398,237,238,431,429,462,450,303)(171,399,400,448,442,461,451,279,280,454,456,441,460,430)(198,422,423,349,452,440,377,316,317,453,387,381,370,252)(218,414,435,322,390,457,388,301,342,392,270,427,436,268)(223,367,438,417,368,262,391,235,350,447,412,449,305,272)(233,425,426,378,360,437,292,364,318,401,384,443,346,411)(265,418,366,315,439,433,434,312,385,446,353,421,341,403)(464,465,466,467);(1,2,5,11,24,51,105,92,168,275,375,451,428,423,452,380,338,173,283,319,425,316,195,312,119,212,238,323,429,230,360,232,363,307,62,122,215,339,432,462,458,189,303,397,276,364,231,150,78,37,16,6,13,29,61,120,57,114,44,90,165,272,392,369,434,386,284,174,94,172,282,395,251,243,328,60,118,136,200,322,130,229,151,257,383,309,415,228,358,441,419,461,342,436,426,399,446,326,279,169,91,43,19,41,84,157,167,258,152,20,42,87,161,268,334,340,299,404,121,176,286,206,327,246,141,202,28,58,70,134,235,67,129,79,149,254,374,450,427,421,447,437,344,217,341,317,424,456,350,409,273,178,97,46,95,52,107,191,242,261,154,260,148,252,378,211,333,186,297,406,288,347,329,237,135,69,32,12,26,33,68,131,55,110,38,77,146,244,373,321,314,410,444,357,293,412,197,315,351,222,349,263,298,185,100,182,124,218,104,190,305,239,370,227,356,400,418,411,101,184,295,393,449,325,302,240,139,73,35,72,14,31,64,25,53,17,36,74,140,241,236,368,290,408,294,181,292,385,454,355,354,440,156,262,247,188,301,65,126,50,102,187,266,387,128,225,353,311,417,221,348,362,445,416,203,324,371,249,145,75,142,108,196,89,66,54,7,15,34,71,137,210,331,179,289,407,296,345,264,384,377,250,376,83,155,143,245,193,30,63,23,48,99,180,291,367,448,365,422,433,125,220,346,438,439,390,455,306,379,253,147,226,127,223,205,132,115,56,112,76,144,248,117,208,98,177,287,405,219,343,388,267,159,85,40,81,153,259,160,138,82,10,21,45,93,171,234,366,280,401,457,414,460,359,442,352,269,389,194,310,382,255,332,163,270,113,204,209,116,207,199,320,277,396,281,47,96,175,285,403,431,435,391,271,164,88,162,111,201,86,59,27,4,8,18,39,80,133,233,170,278,398,300,413,459,463,224,337,214,106,192,308,361,443,313,420,213,336,330,158,265,109,198,318,372,402,123,216,256,381,453,335,430,304,394,274,166,183,103,49,22,9,3)Polycyclic presentation:
2,7,463,2|a^2=d,c^a=c^462,c^b=c^41294 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12964, 2);