Finite Group DatabasebetaFinite Group Databasebeta| order | 7365 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C491⋊C5 |
| unambiguous semidirect product | C491⋊(C3×C5) |
| unambiguous semidirect product | (C3×C491)⋊C5 |
| Fitting, socle, Hall | C3×C491 ⋊ C5 |
| derived, Sylow | C491 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C491⋊C5 |
| commutator, hypocenter | C491 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C491 | C5 |
| LCS | G ▷ C491 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
309 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×C491⋊C5, C3×D491⋊C5, D3×C491⋊C5, … |
| maximal normal subgroup of | C2×C3×C491⋊C5, C3×D491⋊C5, D3×C491⋊C5, … |
| maximal quotient of | C2×C3×C491⋊C5, C9×C491⋊C5, C32×C491⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7365, 1);