Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C2×#10617506 |
| unambiguous semidirect product | D5⋊#2308 |
| Fitting | C23×C5×D4 ⋊ C4 |
| Sylow | C5 ⋊ C2×#2308 |
8142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | #72253753, AGL(1,𝔽5)×#2308, #72269453 |
| maximal normal subgroup of | #72253753, AGL(1,𝔽5)×#2308, #72269453 |
| maximal quotient of | #72253762 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114151);