Finite Group DatabasebetaFinite Group Databasebeta| order | 24156 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C11×C61 · Schur multiplier (H2) = C2×C3 |
| Fitting, socle | C22×C3×C11×C61 ⋊ C3 |
| derived, Sylow | C22 ⋊ C32×C11×C61 |
| Hall | C22×C11×C61 ⋊ C32 |
| Hall | C22×C61 ⋊ C32×C11 |
| Hall | C22×C11 ⋊ C32×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11×C61 | A4 |
| commutator, cosocle, hypocenter | C22 | C32×C11×C61 |
| Frattini | C1 | G |
| Fitting, socle | C22×C3×C11×C61 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C3×C11×C61 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8052 |
8052 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24156, 116);