Finite Group DatabasebetaFinite Group Databasebeta| order | 23994 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D3999 |
| unambiguous semidirect product | C3⋊(C3×D1333) |
| Fitting, socle, Hall | C32×C31×C43 ⋊ C2 |
| derived | C3×C31×C43 ⋊ C2×C3 |
| Hall | C31×C43 ⋊ C3×D3 |
| Hall | C32×C43 ⋊ D31 |
| Hall | C32×C31 ⋊ D43 |
| Sylow | C43 ⋊ C3×D93 |
| Sylow | C31 ⋊ C3×D129 |
| Sylow | C32 ⋊ D1333 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3999 |
| commutator, cosocle, hypocenter | C3×C31×C43 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C31×C43 | C2 |
| LCS | G ▷ C3×C31×C43 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7998 |
6003 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23994, 68);