Finite Group DatabasebetaFinite Group Databasebeta| order | 23406 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×D249 |
| unambiguous semidirect product | C3⋊(C47×D83) |
| unambiguous semidirect product | C83⋊(D3×C47) |
| Fitting, socle, Hall | C3×C47×C83 ⋊ C2 |
| derived, Hall | C3×C83 ⋊ C2×C47 |
| Hall | C47×C83 ⋊ D3 |
| Hall | C3×C47 ⋊ D83 |
| Sylow | C83 ⋊ D3×C47 |
| Sylow | C3 ⋊ C47×D83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | D249 |
| commutator, cosocle, hypocenter | C3×C83 | C2×C47 |
| Frattini | C1 | G |
| Fitting, socle | C3×C47×C83 | C2 |
| LCS | G ▷ C3×C83 | |
| UCS | C1 ◁ C47 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11703 |
5922 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23406, 6);