Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
| direct product | AGL(1,𝔽5)×#543 |
| Fitting | C5×#543 ⋊ C4 |
| Sylow | C5 ⋊ C4×#543 |
2602 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3490, AGL(1,𝔽5)×#543⋊C3, AGL(1,𝔽5)×#2032 |
| maximal normal subgroup of | AGL(1,𝔽5)×#3490, AGL(1,𝔽5)×#543⋊C3, AGL(1,𝔽5)×#2032 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114207);