Finite Group DatabasebetaFinite Group Databasebeta| order | 24318 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#22549230 |
| Fitting, socle, derived | C3×C7×C193 ⋊ C2×C3 |
| Hall | C3×#16860995 ⋊ C2 |
| Hall | C7×C193 ⋊ C3×D3 |
| Sylow | C193 ⋊ C3⋊AGL(1,𝔽7) |
| Sylow | C7 ⋊ D3×C193⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C193 | C2×C3 |
| LCS | G ▷ C3×C7×C193 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 203 |
| transitive degree | μt(G) = 4053 |
A minimal faithful permutation representation — 2 generators on 203 points:
(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,70)(41,56,67)(44,59,64)(47,62,61)(50,65,58)(52,68,55)(54,72,92)(57,75,89)(60,78,86)(63,81,83)(66,84,80)(69,87,77)(71,90,74)(73,94,97)(76,96,113)(79,99,110)(82,102,107)(85,105,104)(88,108,101)(91,111,98)(93,114,95)(100,119,133)(103,122,130)(106,125,127)(109,128,124)(112,131,121)(115,134,118)(116,120,117)(123,139,150)(126,142,147)(129,145,144)(132,148,141)(135,151,138)(136,140,137)(143,156,164)(146,159,161)(149,162,158)(152,165,155)(153,157,154)(160,170,175)(163,173,172)(166,176,169)(167,171,168)(174,181,183)(177,184,180)(178,182,179)(185,189,188)(186,190,187)(191,193,192)(195,198,199,196,197,200)(202,203);(1,2,4,8,15,25,38,54,73,72,93,115,135,152,166,177,185,190,176,148,108,65,33,12,19,29,42,58,77,98,118,137,119,75,37,52,69,88,109,129,146,160,171,151,111,68,35,48,64,83,104,124,141,155,168,156,122,78,40,14,23,34,47,63,82,103,123,140,114,70,89,110,130,147,161,172,180,187,181,159,125,81,43,17,3,6,11,18,28,41,57,76,97,94,116,136,153,167,178,186,191,193,184,162,128,84,46,20,5,9,16,26,39,55,74,95,117,96,53,71,91,112,132,149,163,174,182,165,131,87,49,22,32,45,61,80,101,121,138,154,139,99,56,24,36,50,66,85,106,126,143,157,134,90,51,67,86,107,127,144,158,169,179,170,142,102,59,27,7,13,21,31,44,60,79,100,120,92,113,133,150,164,175,183,188,192,189,173,145,105,62,30,10)(194,195,197,200,199,198,196)(201,202,203)Polycyclic presentation:
2,3^2,7,193|c^a=c^2,d^a=d^6,d^b=d^2,e^b=e^84780 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24318, 47);