Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| isoclinism | isoclinic class of C41⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C22×C32×C41⋊C5 |
| unambiguous semidirect product | (C22×C32×C41)⋊C5 |
| Fitting, socle, Hall | C22×C32×C41 ⋊ C5 |
| derived, Sylow | C41 ⋊ C22×C32×C5 |
| Hall | C32×C41 ⋊ C22×C5 |
| Hall | C22×C41 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32 | C41⋊C5 |
| commutator, hypocenter | C41 | C22×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C41 | C5 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C22×C32 | |
120 conjugacy classes of subgroups.
468 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C32×D5×C41⋊C5, C22×C32×C5×C41⋊C5 |
| maximal normal subgroup of | C22×C32×C5×C41⋊C5 |
| maximal quotient of | C22×C32×C41⋊C25, C2×C32×D5×C41⋊C5, C22×C32×C5×C41⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 85);