Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D15×D123 |
| Fitting, socle, derived, Hall | C32×C5×C41 ⋊ C22 |
| Hall | C32×C41 ⋊ C2×D5 |
| Hall | C5×C41 ⋊ D32 |
| Hall | C32×C5 ⋊ C2×D41 |
| Sylow | C41 ⋊ D3×D15 |
| Sylow | C32 ⋊ D5×D41 |
| Sylow | C5 ⋊ D3×D123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C41 | C22 |
| LCS | G ▷ C32×C5×C41 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
567 conjugacy classes — view the full character table.
| maximal subgroup of | D75×D123, D15×C3⋊(D41⋊C5), C5×D15×D123, … |
| maximal normal subgroup of | D15×C3⋊(D41⋊C5), C5×D15×D123 |
| maximal quotient of | D75×D123, C5×D15×D123, D15×D615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 123);