Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| isoclinism | isoclinic class of #3993 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×#3993 |
| unambiguous semidirect product | D5⋊(C22×#106) |
| Fitting | C23×C5×C8 ⋊ C4 |
| Sylow | C5 ⋊ C23×#106 |
3614 conjugacy classes of subgroups; only the 1464 normal subgroups are shown.
This group has 3614 conjugacy classes of subgroups — too many to draw. Only its 1464 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114793);