Finite Group DatabasebetaFinite Group Databasebeta| order | 23422 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7 |
| direct product | C7×D239⋊C7 |
| unambiguous semidirect product | D239⋊C72 |
| unambiguous semidirect product | (C239⋊C7)⋊(C2×C7) |
| unambiguous semidirect product | (C7×D239)⋊C7 |
| Fitting, socle | C7×C239 ⋊ C2×C7 |
| derived, Sylow | C239 ⋊ C2×C72 |
| Hall | C7×C239⋊C7 ⋊ C2 |
| Hall | D239 ⋊ C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D239⋊C7 |
| commutator, cosocle, hypocenter | C239 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C7×C239 | C2×C7 |
| LCS | G ▷ C239 | |
| UCS | C1 ◁ C7 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1673 |
217 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23422, 8);