Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210×C4 |
| direct product | C2×#10605318 |
| Fitting | C2×C4×C5×C22⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ C2×#2433 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D5 |
| commutator, cosocle | C23×C5 | C25 |
| Frattini | C23 | C24×D5 |
| Fitting | C2×C4×C5×C22⋊C4 | C2 |
| socle | C24×C5 | C24 |
| hypercenter | C2×C4×C22⋊C4 | D5 |
| hypocenter | C5 | C2×#2433 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C24 ◁ C2×C4×C22⋊C4 | |
9422 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
236 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 337389);