Finite Group DatabasebetaFinite Group Databasebeta| order | 7332 |
| isoclinism | isoclinic class of C3⋊#261 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C47 · Schur multiplier (H2) = C1 |
| direct product | C47×C3⋊#261 |
| unambiguous semidirect product | C3⋊(C47×#261) |
| Fitting, socle, Hall | C3×C13×C47 ⋊ C4 |
| derived, Hall | C3×C13 ⋊ C4×C47 |
| Hall | C13×C47 ⋊ Dic3 |
| Hall | C3×C47 ⋊ #261 |
| Sylow | C13 ⋊ Dic3×C47 |
| Sylow | C3 ⋊ C47×#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | C3⋊#261 |
| commutator, hypocenter | C3×C13 | C4×C47 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C47 | C4 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C47 | |
24 conjugacy classes of subgroups.
705 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7332, 24);