Finite Group DatabasebetaFinite Group Databasebeta| order | 23606 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×D319 |
| unambiguous semidirect product | C11⋊(C37×D29) |
| unambiguous semidirect product | C29⋊(D11×C37) |
| Fitting, socle, Hall | C11×C29×C37 ⋊ C2 |
| derived, Hall | C11×C29 ⋊ C2×C37 |
| Hall | C29×C37 ⋊ D11 |
| Hall | C11×C37 ⋊ D29 |
| Sylow | C29 ⋊ D11×C37 |
| Sylow | C11 ⋊ C37×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | D319 |
| commutator, cosocle, hypocenter | C11×C29 | C2×C37 |
| Frattini | C1 | G |
| Fitting, socle | C11×C29×C37 | C2 |
| LCS | G ▷ C11×C29 | |
| UCS | C1 ◁ C37 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11803 |
5957 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23606, 7);