Finite Group DatabasebetaFinite Group Databasebeta| order | 23994 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C31 · Schur multiplier (H2) = C3 |
| direct product | C3×C31×D43⋊C3 |
| unambiguous semidirect product | D43⋊(C32×C31) |
| unambiguous semidirect product | (C43⋊C3)⋊(C2×C3×C31) |
| unambiguous semidirect product | (C3×D43)⋊(C3×C31) |
| Fitting, socle | C3×C31×C43 ⋊ C2×C3 |
| derived, Sylow | C43 ⋊ C2×C32×C31 |
| Hall | C3×C31×C43⋊C3 ⋊ C2 |
| Hall | C31×D43 ⋊ C32 |
| Hall | C31×C43 ⋊ C2×C32 |
| Hall | C3×C43⋊C3 ⋊ C2×C31 |
| Hall | D43 ⋊ C32×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C31 | D43⋊C3 |
| commutator, cosocle, hypocenter | C43 | C2×C32×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C31×C43 | C2×C3 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C3×C31 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3999 |
1209 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23994, 30);