Finite Group DatabasebetaFinite Group Databasebeta| order | 24582 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊(D241⋊C3) |
| unambiguous semidirect product | (C241⋊C3)⋊D17 |
| unambiguous semidirect product | D4097⋊C3 |
| Fitting, socle, derived, Hall | C17×C241 ⋊ C2×C3 |
| Hall | C17×C241⋊C3 ⋊ C2 |
| Hall | D4097 ⋊ C3 |
| Hall | C241⋊C3 ⋊ D17 |
| Sylow | C241 ⋊ C3×D17 |
| Sylow | C17 ⋊ D241⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C241 | C2×C3 |
| LCS | G ▷ C17×C241 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 258 |
| transitive degree | μt(G) = 4097 |
A minimal faithful permutation representation — 2 generators on 258 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)(74,133,134,101,102,167)(76,131,132,104,100,125)(79,94,130,106,107,126)(85,144,145,113,114,121)(89,151,149,118,119,116)(92,156,142,122,123,110)(103,172,173,136,137,205)(105,170,171,138,135,164)(108,129,169,139,140,165)(115,179,180,146,147,160)(120,184,185,152,153,155)(124,190,182,157,158,150)(127,195,177,161,162,143)(141,168,206,174,175,203)(148,207,210,176,181,199)(154,213,214,186,187,194)(159,217,215,191,192,189)(163,222,211,196,197,183)(166,227,208,200,201,178)(188,231,232,209,204,226)(193,235,236,218,219,221)(198,238,233,223,224,216)(202,239,220,228,229,212)(225,240,241,234,230,237)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)(257,258);(1,2,5,11,19,32,51,74,103,138,104,75,52,33,20,4,8,13,23,37,56,79,108,141,176,146,113,83,58,36,10,16,24,38,57,81,110,143,178,209,186,152,118,87,55,18,29,39,41,61,86,116,150,183,212,218,191,157,122,78,31,48,59,62,64,90,121,155,189,216,234,223,196,161,107,50,71,84,88,91,93,125,160,194,221,237,240,228,200,140,73,100,114,119,123,126,128,164,199,226,239,238,235,231,175,102,135,147,153,158,162,165,167,173,206,227,222,217,213,207,137,172,181,187,192,197,201,203,205,134,169,195,190,184,179,170,133,168,204,219,224,229,232,210,171,99,130,156,151,144,131,98,129,166,202,230,241,236,214,180,132,70,95,117,111,96,69,94,127,163,198,225,233,215,185,145,97,47,66,82,67,46,65,92,124,159,193,220,211,182,149,112,68,28,43,44,27,42,63,89,120,154,188,208,177,142,109,80,45,15,26,14,25,40,60,85,115,148,174,139,106,77,54,35,22,7,6,12,21,34,53,76,105,136,101,72,49,30,17,9,3)(242,243,245,247,249,251,253,255,257,258,256,254,252,250,248,246,244)Polycyclic presentation:
2,3,17,241|c^a=c^16,d^a=d^240,d^b=d^15710 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24582, 12);