Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C22 |
| direct product | C2×C9×#700 |
| Hall | C5×C9 ⋊ C2×M16 |
| Sylow | C5 ⋊ C2×C9×M16 |
204 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 720 |
252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1544);