Finite Group DatabasebetaFinite Group Databasebeta| order | 24966 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#22552248 |
| Fitting, socle, derived | C3×C19×C73 ⋊ C2×C3 |
| Hall | C3×#16861932 ⋊ C2 |
| Hall | C19×C73 ⋊ C3×D3 |
| Sylow | C73 ⋊ C3⋊(D19⋊C3) |
| Sylow | C19 ⋊ D3×C73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C19×C73 | C2×C3 |
| LCS | G ▷ C3×C19×C73 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 95 |
| transitive degree | μt(G) = 4161 |
A minimal faithful permutation representation — 2 generators on 95 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)(25,37,50)(28,40,47)(31,43,45)(34,38,42)(36,48,39)(41,53,62)(44,56,60)(46,54,58)(49,61,55)(51,63,52)(57,66,70)(59,67,69)(64,71,65)(68,72,73)(75,79,80,76,77,81)(78,87,84,82,83,89)(85,90,92,91,88,86)(94,95);(1,2,4,8,15,25,38,20,5,9,16,26,39,52,61,33,12,19,29,42,55,65,71,48,22,32,45,58,37,51,64,63,35,47,60,69,53,24,36,49,50,62,70,73,66,40,14,23,34,46,59,68,72,56,27,7,13,21,31,44,57,67,43,17,3,6,11,18,28,41,54,30,10)(74,75,78,84,90,87,91,77,81,86,92,80,79,85,83,88,89,82,76)(93,94,95)Polycyclic presentation:
2,3^2,19,73|c^a=c^2,d^a=d^18,d^b=d^7,e^b=e^64738 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24966, 96);