Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#64864 |
| Fitting | C22×C5×C22⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ C22×AΣL(1,𝔽16) |
2774 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 2774 conjugacy classes of subgroups — too many to draw. Only its 240 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
92 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1113453);