Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C2×D42×D5 |
| Fitting | C2×C5×D42 ⋊ C2 |
| Sylow | C5 ⋊ C22×D42 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C24×D5 |
| commutator, cosocle | C22×C5 | C26 |
| Frattini | C22 | C25×D5 |
| Fitting | C2×C5×D42 | C2 |
| socle | C23×C5 | C25 |
| hypercenter | C2×D42 | D5 |
| hypocenter | C5 | C22×D42 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ C2×D42 | |
20038 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D42×AGL(1,𝔽5) |
| maximal normal subgroup of | C2×D42×AGL(1,𝔽5) |
| maximal quotient of | D5×#61110 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1076474);