Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| isoclinism | isoclinic class of #564⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C22×#564⋊C5 |
| unambiguous semidirect product | (C22×#564)⋊C5 |
| Fitting, Sylow | C22×#564 ⋊ C5 |
| derived | #564 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C24 | C24⋊C5 |
| commutator, cosocle, hypocenter | #564 | C22×C5 |
| Frattini | C22 | C22×C24⋊C5 |
| Fitting | C22×#564 | C5 |
| LCS | G ▷ #564 | |
| UCS | C1 ◁ C24 | |
767 conjugacy classes of subgroups.
| transitive degree | μt(G) = 256 |
92 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116325);