Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D369 |
| unambiguous semidirect product | (C9×D5)⋊D41 |
| unambiguous semidirect product | (D5×C41)⋊D9 |
| Fitting, derived, Hall | C5×C9×C41 ⋊ C22 |
| Hall | C9×C41 ⋊ C2×D5 |
| Hall | C5×C41 ⋊ C2×D9 |
| Hall | C5×C9 ⋊ C2×D41 |
| Sylow | C41 ⋊ D5×D9 |
| Sylow | C9 ⋊ D5×D41 |
| Sylow | C5 ⋊ C2×D369 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C9×C41 | C22 |
| Frattini | C3 | D5×D123 |
| socle | C3×C5×C41 | C2×D3 |
| LCS | G ▷ C5×C9×C41 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
744 conjugacy classes — view the full character table.
| maximal subgroup of | D25×D369, D5×C9⋊(D41⋊C5), C5×D5×D369, … |
| maximal normal subgroup of | D5×C9⋊(D41⋊C5), C5×D5×D369 |
| maximal quotient of | D25×D369, C5×D5×D369, C5⋊D5×D369, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 38);