Finite Group DatabasebetaFinite Group Databasebeta| order | 23452 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C13×D11×D41 |
| unambiguous semidirect product | (D11×C41)⋊(C2×C13) |
| unambiguous semidirect product | (C11×D41)⋊(C2×C13) |
| unambiguous semidirect product | D451⋊(C2×C13) |
| Fitting, socle, Hall | C11×C13×C41 ⋊ C22 |
| derived, Hall | C11×C41 ⋊ C22×C13 |
| Hall | C13×C41 ⋊ C2×D11 |
| Hall | C11×C13 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×C13×D11 |
| Sylow | C11 ⋊ C2×C13×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D11×D41 |
| commutator, cosocle, hypocenter | C11×C41 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C11×C13×C41 | C22 |
| LCS | G ▷ C11×C41 | |
| UCS | C1 ◁ C13 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5863 |
2002 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23452, 18);