Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D5×#360 |
| Fitting | C2×C5×#360 ⋊ C2 |
| Sylow | C5 ⋊ C22×#360 |
1214 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×#360, C2×D5×AGL(1,ℤ/16), C2×#13025928, … |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#360, C2×D5×AGL(1,ℤ/16), C2×#13025928 |
| maximal quotient of | C2×C5⋊D5×#360 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 322503);