Finite Group DatabasebetaFinite Group Databasebeta| order | 23358 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊(D229⋊C3) |
| unambiguous semidirect product | (C229⋊C3)⋊D17 |
| unambiguous semidirect product | D3893⋊C3 |
| Fitting, socle, derived, Hall | C17×C229 ⋊ C2×C3 |
| Hall | C17×C229⋊C3 ⋊ C2 |
| Hall | D3893 ⋊ C3 |
| Hall | C229⋊C3 ⋊ D17 |
| Sylow | C229 ⋊ C3×D17 |
| Sylow | C17 ⋊ D229⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C229 | C2×C3 |
| LCS | G ▷ C17×C229 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 246 |
| transitive degree | μt(G) = 3893 |
A minimal faithful permutation representation — 2 generators on 246 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)(103,174,175,136,137,209)(105,172,173,139,135,166)(108,129,171,141,142,167)(115,186,178,148,149,162)(120,192,193,154,155,157)(124,198,190,159,160,152)(127,201,184,163,164,145)(138,194,195,177,156,221)(140,211,212,179,176,207)(143,170,210,181,182,208)(150,217,214,187,188,204)(161,224,183,199,200,197)(165,225,216,202,203,191)(168,226,215,205,206,185)(180,222,223,213,196,228)(189,229,220,218,219,227)(231,232)(233,234)(235,236)(237,238)(239,240)(241,242)(243,244)(245,246);(1,2,5,11,19,32,51,74,103,138,178,132,70,95,117,111,96,69,94,127,165,182,102,135,149,155,160,164,167,169,207,227,218,187,148,113,83,58,36,10,16,24,38,57,81,110,145,185,216,190,151,112,68,28,43,44,27,42,63,89,120,156,196,219,223,175,210,226,225,224,221,217,211,174,199,159,122,78,31,48,59,62,64,90,121,157,197,181,141,106,77,54,35,22,7,6,12,21,34,53,76,105,140,180,214,173,99,130,158,153,146,131,98,129,168,205,142,73,100,114,119,123,126,128,166,204,213,179,139,104,75,52,33,20,4,8,13,23,37,56,79,108,143,183,193,147,97,47,66,82,67,46,65,92,124,161,137,176,188,195,200,203,206,208,209,228,229,222,194,154,118,87,55,18,29,39,41,61,86,116,152,191,215,184,144,109,80,45,15,26,14,25,40,60,85,115,150,189,220,212,134,171,201,198,192,186,172,133,170,202,163,107,50,71,84,88,91,93,125,162,177,136,101,72,49,30,17,9,3)(230,231,233,235,237,239,241,243,245,246,244,242,240,238,236,234,232)Polycyclic presentation:
2,3,17,229|c^a=c^16,d^a=d^228,d^b=d^134676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23358, 12);