Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| isoclinism | isoclinic class of C24⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C28 |
| direct product | C24×C24⋊C5 |
| Fitting, socle, Sylow | C28 ⋊ C5 |
| derived | C24 ⋊ C24×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | C24⋊C5 |
| commutator, cosocle, hypocenter | C24 | C24×C5 |
| Frattini | C1 | G |
| Fitting, socle | C28 | C5 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C24 | |
83681 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116357);