Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#91563 |
| Hall | C32×C5 ⋊ #120 |
| Sylow | C32 ⋊ #4083 |
| Sylow | C5 ⋊ C3×#953 |
654 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#953, #72269640 |
| maximal normal subgroup of | C3×D5×#953 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 3023);