Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×C5×#3752 |
| Fitting | C22×C32×C4×C5 ⋊ C2 |
| Hall | C32×C5 ⋊ C2×C22⋊C4 |
| Sylow | C32 ⋊ C2×C5×C22⋊C4 |
792 conjugacy classes of subgroups; only the 266 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 266 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 720 |
420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4427);