Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| isoclinism | isoclinic class of C24⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C8×C24⋊C5 |
| unambiguous semidirect product | (C25×C8)⋊C5 |
| Fitting, Sylow | C25×C8 ⋊ C5 |
| derived | C24 ⋊ C2×C5×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | C24⋊C5 |
| commutator, hypocenter | C24 | C2×C5×C8 |
| Frattini | C4 | C22×C24⋊C5 |
| Fitting | C25×C8 | C5 |
| socle | C26 | C4×C5 |
| prime radical | C22×C24⋊C5 | C4 |
| cosocle | C24×C4 | C22×C5 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C2×C8 | |
1585 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 1585 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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, 1116337);