Finite Group DatabasebetaFinite Group Databasebeta| order | 7380 |
| isoclinism | isoclinic class of #4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3 |
| direct product | C32×C5×#4223 |
| Fitting, socle, Hall | C32×C5×C41 ⋊ C4 |
| derived, Sylow | C41 ⋊ C32×C4×C5 |
| Hall | C32×C41 ⋊ C4×C5 |
| Hall | C5×C41 ⋊ C32×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5 | #4223 |
| commutator, hypocenter | C41 | C32×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C41 | C4 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C32×C5 | |
72 conjugacy classes of subgroups.
630 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7380, 86);