Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#91562 |
| Hall | C32×C5 ⋊ #123 |
| Sylow | C32 ⋊ #4029 |
| Sylow | C5 ⋊ C3×#883 |
346 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 92 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, 3022);