Finite Group DatabasebetaFinite Group Databasebeta| order | 24156 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D33×D61⋊C3 |
| unambiguous semidirect product | D61⋊(C3×D33) |
| unambiguous semidirect product | (C3×D61⋊C3)⋊D11 |
| unambiguous semidirect product | (C11×D61⋊C3)⋊D3 |
| unambiguous semidirect product | (D33×D61)⋊C3 |
| Fitting, socle, derived | C3×C11×C61 ⋊ C22×C3 |
| Hall | C3×C11×C61⋊C3 ⋊ C22 |
| Hall | C11×C61 ⋊ C2×C3×D3 |
| Hall | C3×C61⋊C3 ⋊ C2×D11 |
| Sylow | C61 ⋊ C2×C3×D33 |
| Sylow | C11 ⋊ D3×D61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C61 | C22×C3 |
| LCS | G ▷ C3×C11×C61 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2013 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24156, 68);