Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D5×#3717 |
| Hall | C32×C5 ⋊ C2×SD16 |
| Sylow | C32 ⋊ D5×SD16 |
| Sylow | C5 ⋊ C2×#3717 |
326 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#63930, D5×#63937, AGL(1,𝔽5)×#3717, … |
| maximal normal subgroup of | D5×#63930, D5×#63937, AGL(1,𝔽5)×#3717, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1999);