Finite Group DatabasebetaFinite Group Databasebeta| order | 9338 |
| isoclinism | isoclinic class of C29⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C23 · Schur multiplier (H2) = C1 |
| direct product | C2×C23×C29⋊C7 |
| unambiguous semidirect product | (C2×C29)⋊(C7×C23) |
| unambiguous semidirect product | (C2×C23×C29)⋊C7 |
| Fitting, socle, Hall | C2×C23×C29 ⋊ C7 |
| derived, Sylow | C29 ⋊ C2×C7×C23 |
| Hall | C23×C29 ⋊ C2×C7 |
| Hall | C2×C29 ⋊ C7×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C23 | C29⋊C7 |
| commutator, hypocenter | C29 | C2×C7×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C23×C29 | C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2×C23 | |
16 conjugacy classes of subgroups.
506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9338, 2);