Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | D5×#2196 |
| Fitting | C5×#2196 ⋊ C2 |
| Sylow | C5 ⋊ C2×#2196 |
1956 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 1956 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
80 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#2196, #72242930, D5×#73026 |
| maximal normal subgroup of | D5×#33551, AGL(1,𝔽5)×#2196, #72242930 |
| maximal quotient of | D5×#13343 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 323566);