Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D5×GO+(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D5×D32⋊C4 |
| Hall | C32×C5 ⋊ C2×C22⋊C4 |
| Sylow | C32 ⋊ D5×C22⋊C4 |
| Sylow | C5 ⋊ C2×D32⋊C4 |
452 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 452 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) = 60 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×D32⋊C4, D5×#64241, #72269747 |
| maximal normal subgroup of | AGL(1,𝔽5)×D32⋊C4, D5×#64241, #72269747 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4758);