Finite Group DatabasebetaFinite Group Databasebeta| order | 25014 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(D379⋊C3) |
| unambiguous semidirect product | (C379⋊C3)⋊D11 |
| unambiguous semidirect product | D4169⋊C3 |
| Fitting, socle, derived, Hall | C11×C379 ⋊ C2×C3 |
| Hall | C11×C379⋊C3 ⋊ C2 |
| Hall | D4169 ⋊ C3 |
| Hall | C379⋊C3 ⋊ D11 |
| Sylow | C379 ⋊ C3×D11 |
| Sylow | C11 ⋊ D379⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C379 | C2×C3 |
| LCS | G ▷ C11×C379 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 390 |
| transitive degree | μt(G) = 4169 |
A minimal faithful permutation representation — 2 generators on 390 points:
(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,64)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,69,70,49,50,93)(34,67,68,52,48,61)(37,42,66,54,55,62)(40,82,80,58,59,57)(51,98,99,72,73,128)(53,96,97,75,71,90)(56,65,95,77,78,91)(60,111,112,83,84,86)(63,117,109,87,88,81)(74,133,134,101,102,169)(76,131,132,104,100,125)(79,94,130,106,107,126)(85,146,147,113,114,121)(89,153,151,118,119,116)(92,158,144,122,123,110)(103,174,175,136,137,216)(105,172,173,139,135,166)(108,129,171,141,142,167)(115,187,188,148,149,162)(120,194,195,154,155,157)(124,200,192,159,160,152)(127,205,185,163,164,145)(138,221,222,177,178,269)(140,219,220,180,176,213)(143,170,218,182,183,214)(150,234,235,189,190,209)(156,241,242,196,197,204)(161,248,246,201,202,199)(165,253,239,206,207,193)(168,258,232,210,211,186)(179,274,275,224,225,326)(181,272,273,227,223,266)(184,217,271,229,230,267)(191,287,288,236,237,262)(198,294,295,243,244,257)(203,301,302,249,250,252)(208,307,299,254,255,247)(212,312,292,259,260,240)(215,317,285,263,264,233)(226,331,332,277,278,370)(228,329,330,280,276,323)(231,270,328,282,283,324)(238,340,341,289,290,319)(245,345,346,296,297,316)(251,349,350,303,304,311)(256,354,352,308,309,306)(261,357,348,313,314,300)(265,334,343,279,318,293)(268,361,338,320,321,286)(281,358,353,315,333,367)(284,327,371,335,336,368)(291,355,356,310,342,363)(298,351,359,305,347,360)(322,372,375,337,362,344)(325,377,373,364,365,339)(366,378,379,374,369,376)(381,382)(383,384)(385,386)(387,388)(389,390);(1,2,5,11,19,32,51,74,103,138,179,226,279,263,183,102,135,149,155,160,164,167,169,213,262,316,359,341,273,175,218,258,253,248,241,234,219,174,217,268,322,335,282,229,182,141,106,77,54,35,22,7,6,12,21,34,53,76,105,140,181,228,281,313,259,210,142,73,100,114,119,123,126,128,166,209,257,311,356,330,222,271,317,312,307,301,294,287,272,221,270,325,366,373,338,285,232,185,144,109,80,45,15,26,14,25,40,60,85,115,150,191,238,291,308,254,206,163,107,50,71,84,88,91,93,125,162,204,252,306,353,275,328,361,334,357,354,349,345,340,329,274,327,369,379,375,343,292,239,192,151,112,68,28,43,44,27,42,63,89,120,156,198,245,298,303,249,201,159,122,78,31,48,59,62,64,90,121,157,199,247,300,332,371,377,372,278,333,342,347,351,355,358,331,362,365,368,370,348,299,246,195,147,97,47,66,82,67,46,65,92,124,161,203,251,305,296,243,196,154,118,87,55,18,29,39,41,61,86,116,152,193,240,293,344,376,378,336,225,276,290,297,304,309,314,318,321,324,326,367,352,302,242,188,132,70,95,117,111,96,69,94,127,165,208,256,310,289,236,189,148,113,83,58,36,10,16,24,38,57,81,110,145,186,233,286,339,374,364,283,178,223,237,244,250,255,260,264,267,269,323,363,350,295,235,173,99,130,158,153,146,131,98,129,168,212,261,315,280,227,180,139,104,75,52,33,20,4,8,13,23,37,56,79,108,143,184,231,284,337,320,230,137,176,190,197,202,207,211,214,216,266,319,360,346,288,220,134,171,205,200,194,187,172,133,170,215,265,277,224,177,136,101,72,49,30,17,9,3)(380,381,383,385,387,389,390,388,386,384,382)Polycyclic presentation:
2,3,11,379|c^a=c^10,d^a=d^378,d^b=d^327714 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25014, 12);