Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C26×C42 |
| direct product | C2×AGL(1,𝔽5)×#95 |
| Fitting | C2×C5×#95 ⋊ C4 |
| Sylow | C5 ⋊ C2×C4×#95 |
4462 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#1437, AGL(1,𝔽5)×#1438, AGL(1,𝔽5)×#1504, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#1437, AGL(1,𝔽5)×#1438, AGL(1,𝔽5)×#1504, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1098152);