Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | AGL(1,𝔽5)×#354 |
| Fitting | C5×#354 ⋊ C4 |
| Sylow | C5 ⋊ C4×#354 |
584 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
65 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#2199, AGL(1,𝔽5)×#2127, AGL(1,𝔽5)×#2197 |
| maximal normal subgroup of | AGL(1,𝔽5)×#2199, AGL(1,𝔽5)×#2127, AGL(1,𝔽5)×#2197 |
| maximal quotient of | AGL(1,𝔽5)×#1393 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1096093);