Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#91549 |
| Hall | C32×C5 ⋊ #121 |
| Sylow | C32 ⋊ #4084 |
| Sylow | C5 ⋊ C3×#939 |
430 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 3024);