Finite Group DatabasebetaFinite Group Databasebeta| order | 23426 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D689 |
| unambiguous semidirect product | C13⋊(C17×D53) |
| unambiguous semidirect product | C53⋊(C17×D13) |
| Fitting, socle, Hall | C13×C17×C53 ⋊ C2 |
| derived, Hall | C13×C53 ⋊ C2×C17 |
| Hall | C17×C53 ⋊ D13 |
| Hall | C13×C17 ⋊ D53 |
| Sylow | C53 ⋊ C17×D13 |
| Sylow | C13 ⋊ C17×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D689 |
| commutator, cosocle, hypocenter | C13×C53 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C13×C17×C53 | C2 |
| LCS | G ▷ C13×C53 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11713 |
5882 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23426, 7);