Finite Group DatabasebetaFinite Group Databasebeta| order | 24966 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#22552252 |
| Fitting, socle, derived | C3×C19×C73 ⋊ C2×C3 |
| Hall | C3×#16861932 ⋊ C2 |
| Hall | C19×C73 ⋊ C3×D3 |
| Sylow | C73 ⋊ C3⋊(D19⋊C3) |
| Sylow | C19 ⋊ C3⋊(D73⋊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:
(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,59)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,51,57,37,42,60)(34,61,62,49,48,56)(40,65,64,53,54,52)(50,70,71,63,58,72)(55,73,68,66,67,69)(75,79,80,76,77,81)(78,87,84,82,83,89)(85,90,92,91,88,86)(94,95);(1,2,5,11,19,32,35,22,7,6,12,21,34,50,64,45,15,26,14,25,40,55,68,62,28,43,44,27,42,58,67,71,47,60,65,61,46,31,48,54,57,59,72,73,70,51,18,29,39,41,56,69,66,53,36,10,16,24,38,52,63,49,33,20,4,8,13,23,37,30,17,9,3)(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,e^a=e^72,d^b=d^7,e^b=e^64702 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24966, 94);