Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C24 |
| direct product | D5×C22⋊C32 |
| Fitting | C5×C22⋊C32 ⋊ C2 |
| Sylow | C5 ⋊ C2×C22⋊C32 |
342 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 89757);