Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C2×#10619182 |
| Fitting | C22×C5×H(5,𝔽2) ⋊ C2 |
| Sylow | C5 ⋊ C2×#3496 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C24×D5 |
| commutator, cosocle | C22×C5 | C26 |
| Frattini | C22 | C25×D5 |
| Fitting | C22×C5×H(5,𝔽2) | C2 |
| socle | C23×C5 | C25 |
| hypercenter | C22×H(5,𝔽2) | D5 |
| hypocenter | C5 | C2×#3496 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ C22×H(5,𝔽2) | |
12378 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1077458);