Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#10603925 |
| unambiguous semidirect product | D5⋊#1856 |
| Fitting | C2×C5×#100 ⋊ C4 |
| Sylow | C5 ⋊ C2×#1856 |
1706 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
86 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221215, C2×AGL(1,𝔽5)×#453, #72221514, … |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#453, #72221514, #72258314 |
| maximal quotient of | C2×#72221215, C2×#72213479, D3×#10603925 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1105040);