Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | AGL(1,𝔽5)×#458 |
| Fitting | C5×#458 ⋊ C4 |
| Sylow | C5 ⋊ C4×#458 |
1538 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 1538 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3025, AGL(1,𝔽5)×#3026, AGL(1,𝔽5)×#2197, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#3025, AGL(1,𝔽5)×#3026, AGL(1,𝔽5)×#2197, … |
| maximal quotient of | AGL(1,𝔽5)×#1790 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1106475);