Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#10604786 |
| unambiguous semidirect product | D5⋊#2140 |
| Fitting | C22×C5×D8 ⋊ C4 |
| Sylow | C5 ⋊ C2×#2140 |
1406 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
92 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×#509, C2×#13025910, C2×#13025913, … |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#509, C2×#13025910, C2×#13025913 |
| maximal quotient of | C2×#72242325 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1113604);