Finite Group DatabasebetaFinite Group Databasebeta| order | 23422 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(D239⋊C7) |
| unambiguous semidirect product | (C239⋊C7)⋊D7 |
| unambiguous semidirect product | D1673⋊C7 |
| Fitting, socle, derived | C7×C239 ⋊ C2×C7 |
| Hall | C7×C239⋊C7 ⋊ C2 |
| Sylow | C239 ⋊ C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C239 | C2×C7 |
| LCS | G ▷ C7×C239 | |
| UCS | C1 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1673 |
Polycyclic presentation:
2,7^2,239|c^a=c^6,d^a=d^238,d^b=d^100154 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23422, 9);