Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×AGL(1,𝔽5)×C4⋊Q8 |
| unambiguous semidirect product | D5⋊(C4×C4⋊Q8) |
| Fitting | C2×C5×C4⋊Q8 ⋊ C4 |
| Sylow | C5 ⋊ C2×C4×C4⋊Q8 |
3358 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×#532 |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#532 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114148);