Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | D32×C41⋊C5 |
| unambiguous semidirect product | (C3×D3)⋊(C2×C41⋊C5) |
| unambiguous semidirect product | (C3⋊D3)⋊(C2×C41⋊C5) |
| unambiguous semidirect product | (D32×C41)⋊C5 |
| Fitting, socle, derived, Hall | C32×C41 ⋊ C22×C5 |
| Hall | C32×C41⋊C5 ⋊ C22 |
| Hall | D32×C41 ⋊ C5 |
| Sylow | C41 ⋊ C5×D32 |
| Sylow | C32 ⋊ C22×C41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C41 | C22×C5 |
| LCS | G ▷ C32×C41 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
117 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D32×C41⋊C5, D3×D15×C41⋊C5, (C3⋊D3)⋊D5×C41⋊C5, … |
| maximal normal subgroup of | C5×D32×C41⋊C5, D32×D41⋊C5 |
| maximal quotient of | D32×C41⋊C25, C5×D32×C41⋊C5, D3×D15×C41⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 75);