Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C216 |
| direct product | C24×C22⋊AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C23×C22⋊C4) |
| unambiguous semidirect product | (C2×AGL(1,𝔽5))⋊C25 |
| Fitting | C26×C5 ⋊ C4 |
| Sylow | C5 ⋊ C24×C22⋊C4 |
43678 conjugacy classes of subgroups; only the 8408 normal subgroups are shown.
This group has 43678 conjugacy classes of subgroups — too many to draw. Only its 8408 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116274);