Finite Group DatabasebetaFinite Group Databasebeta| order | 24156 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| derived, Hall | C11×C61 ⋊ C22×C9 |
| Hall | C11×C61⋊C9 ⋊ C22 |
| Hall | D11×D61 ⋊ C9 |
| Hall | C61⋊C9 ⋊ C2×D11 |
| Sylow | C61 ⋊ C2×C9×D11 |
| Sylow | C11 ⋊ C2×D61⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D11×D61⋊C3 |
| commutator, hypocenter | C11×C61 | C22×C9 |
| Fitting, socle, cosocle | C3×C11×C61 | C22×C3 |
| prime radical | C3×D11×D61 | C3 |
| LCS | G ▷ C11×C61 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6039 |
336 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24156, 16);