Finite Group DatabasebetaFinite Group Databasebeta| order | 23994 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#22547865 |
| Fitting, socle, derived | C3×C31×C43 ⋊ C2×C3 |
| Hall | C3×#16860687 ⋊ C2 |
| Hall | C31×C43 ⋊ C3×D3 |
| Sylow | C43 ⋊ C3⋊(D31⋊C3) |
| Sylow | C31 ⋊ D3×C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C31×C43 | C2×C3 |
| LCS | G ▷ C3×C31×C43 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 3999 |
A minimal faithful permutation representation — 2 generators on 77 points:
(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,30)(18,26,31)(21,29,28)(23,32,25)(27,36,38)(33,39,37)(34,40,35)(41,43,42)(45,49,50,46,47,51)(48,57,58,52,53,65)(54,68,69,60,61,73)(55,67,63,62,59,56)(64,66,74,70,71,72)(76,77);(1,2,4,8,15,17,3,6,11,18,27,26,7,13,21,30,38,36,14,23,33,40,22,31,24,34,41,43,32,12,19,28,37,42,39,20,5,9,16,25,35,29,10)(44,45,48,54,62,47,51,56,64,71,53,59,65,69,74,61,68,72,73,58,67,57,66,70,63,50,49,55,60,52,46)(75,76,77)Polycyclic presentation:
2,3^2,31,43|c^a=c^2,d^a=d^30,d^b=d^5,e^b=e^6696 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23994, 48);