Finite Group DatabasebetaFinite Group Databasebeta| order | 7362 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C2×C3×C409⋊C3 |
| unambiguous semidirect product | (C2×C409)⋊C32 |
| unambiguous semidirect product | (C2×C3×C409)⋊C3 |
| Fitting, socle | C2×C3×C409 ⋊ C3 |
| derived, Sylow | C409 ⋊ C2×C32 |
| Hall | C2×C409 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C409⋊C3 |
| commutator, hypocenter | C409 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C409 | C3 |
| LCS | G ▷ C409 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
834 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7362, 11);