Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D5×GO+(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | Dic5×GO+(4,𝔽2) |
| Hall | C32×C5 ⋊ C4×D4 |
| Sylow | C32 ⋊ D4×Dic5 |
| Sylow | C5 ⋊ C4×GO+(4,𝔽2) |
296 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4760);