Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C32×#686 |
| Fitting | C2×C32×C5×D4 ⋊ C2 |
| Hall | C32×C5 ⋊ C2×D8 |
| Sylow | C5 ⋊ C2×C32×D8 |
456 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 198 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 720 |
306 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4178);