Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #67138 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C4×#67141 |
| Hall | C32×C5 ⋊ C4×Q8 |
| Sylow | C32 ⋊ C4×Dic10 |
| Sylow | C5 ⋊ C4×#634 |
420 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1440 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 3258);