Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#10604090 |
| Fitting | C2×C5×#108 ⋊ C4 |
| Sylow | C5 ⋊ C2×#1773 |
1062 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽5)×#444, C2×#13026054, C2×#13025913, … |
| maximal normal subgroup of | C2×AGL(1,𝔽5)×#444, C2×#13026054, C2×#13025913 |
| maximal quotient of | C2×#72253120 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1103824);