Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| Fitting, derived, Hall | C9×C41 ⋊ C22×C5 |
| Hall | C9×C41⋊C5 ⋊ C22 |
| Hall | D9×D41 ⋊ C5 |
| Hall | C41⋊C5 ⋊ C2×D9 |
| Sylow | C41 ⋊ C2×C5×D9 |
| Sylow | C9 ⋊ C2×D41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C41 | C22×C5 |
| Frattini | C3 | D3×D41⋊C5 |
| socle | C3×C41 | C2×C5×D3 |
| LCS | G ▷ C9×C41 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
84 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D9×D41⋊C5, D45×D41⋊C5, D9×C5⋊(D41⋊C5), … |
| maximal normal subgroup of | C5×D9×D41⋊C5 |
| maximal quotient of | D9×D41⋊C25, C5×D9×D41⋊C5, D45×D41⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 16);