Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C42 |
| direct product | C2×#10617507 |
| unambiguous semidirect product | D5⋊#2309 |
| Fitting | C23×C5×D4 ⋊ C4 |
| Sylow | C5 ⋊ C2×#2309 |
7710 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×#535 |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#535 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114152);