Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×D5×D41 |
| unambiguous semidirect product | (D5×C41)⋊(C2×C32) |
| unambiguous semidirect product | (C5×D41)⋊(C2×C32) |
| unambiguous semidirect product | D205⋊(C2×C32) |
| Fitting, socle, Hall | C32×C5×C41 ⋊ C22 |
| derived, Hall | C5×C41 ⋊ C22×C32 |
| Hall | C32×C41 ⋊ C2×D5 |
| Hall | C32×C5 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×C32×D5 |
| Sylow | C5 ⋊ C2×C32×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D5×D41 |
| commutator, hypocenter | C5×C41 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C41 | C22 |
| LCS | G ▷ C5×C41 | |
| UCS | C1 ◁ C32 | |
120 conjugacy classes of subgroups.
792 conjugacy classes — view the full character table.
| maximal subgroup of | C32×D25×D41, C32×D5×D41⋊C5, C32×C5×D5×D41, … |
| maximal normal subgroup of | C32×D5×D41⋊C5, C32×C5×D5×D41 |
| maximal quotient of | C32×D25×D41, C32×C5×D5×D41, C32×D5×D205, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 92);