Finite Group DatabasebetaFinite Group Databasebeta| order | 23422 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D239⋊C49 |
| unambiguous semidirect product | (C239⋊C49)⋊C2 |
| derived, Sylow | C239 ⋊ C2×C49 |
| Hall | C239⋊C49 ⋊ C2 |
| Hall | D239 ⋊ C49 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C7 | D239⋊C7 |
| commutator, hypocenter | C239 | C2×C49 |
| Fitting, socle, cosocle | C7×C239 | C2×C7 |
| prime radical | C7×D239 | C7 |
| LCS | G ▷ C239 | |
| UCS | C1 ◁ C7 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11711 |
Polycyclic presentation:
2,7,239,7|b^7=d,c^a=c^238,c^b=c^24217 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23422, 2);