Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | M16×C24⋊C5 |
| unambiguous semidirect product | (C24×M16)⋊C5 |
| Fitting, Sylow | C24×M16 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×C24⋊C5 |
| commutator, socle | C25 | C2×C4×C5 |
| Fitting | C24×M16 | C5 |
| prime radical | C22×C24⋊C5 | C4 |
| cosocle | C24×C4 | C22×C5 |
| hypercenter | M16 | C24⋊C5 |
| hypocenter | C24 | C5×M16 |
| LCS | G ▷ C25 ▷ C24 | |
| UCS | C1 ◁ C4 ◁ M16 | |
1367 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 1367 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116338);