Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | Dic9×C41⋊C5 |
| unambiguous semidirect product | C9⋊(C4×C41⋊C5) |
| unambiguous semidirect product | (Dic9×C41)⋊C5 |
| derived, Hall | C9×C41 ⋊ C4×C5 |
| Hall | C9×C41⋊C5 ⋊ C4 |
| Hall | Dic9×C41 ⋊ C5 |
| Sylow | C41 ⋊ C5×Dic9 |
| Sylow | C9 ⋊ C4×C41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9×C41⋊C5 |
| commutator, hypocenter | C9×C41 | C4×C5 |
| Frattini | C2×C3 | D3×C41⋊C5 |
| Fitting | C2×C9×C41 | C2×C5 |
| socle | C2×C3×C41 | C5×D3 |
| LCS | G ▷ C9×C41 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
156 conjugacy classes — view the full character table.
| maximal subgroup of | C5×Dic9×C41⋊C5, Dic45×C41⋊C5, C9⋊AGL(1,𝔽5)×C41⋊C5 |
| maximal normal subgroup of | C5×Dic9×C41⋊C5 |
| maximal quotient of | Dic9×C41⋊C25, C5×Dic9×C41⋊C5, Dic45×C41⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 3);