Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C26×C43 |
| direct product | C2×#10614912 |
| Fitting | C22×C5×#127 ⋊ C2 |
| Sylow | C5 ⋊ C2×#2657 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D5 |
| commutator, cosocle | C23×C5 | C25 |
| Frattini | C23 | C24×D5 |
| Fitting | C22×C5×#127 | C2 |
| socle | C24×C5 | C24 |
| hypercenter | C22×#127 | D5 |
| hypocenter | C5 | C2×#2657 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C24 ◁ C22×#127 | |
5142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 336737);