Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C22×#65699 |
| unambiguous semidirect product | D5⋊(C2×#385) |
| Fitting | C22×C5×C22⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ C22×#385 |
8670 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | C22×AGL(1,𝔽5)×#120, #72221500, #72242746, … |
| maximal normal subgroup of | C22×AGL(1,𝔽5)×#120, #72221500, #72242746, … |
| maximal quotient of | #72269442, #72269813 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114124);