Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #6706 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×#91089 |
| Fitting | C32×C42×C5 ⋊ C2 |
| Hall | C32×C5 ⋊ #104 |
| Sylow | C32 ⋊ #3937 |
| Sylow | C5 ⋊ C3×#805 |
206 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
378 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D5×#805, #72260139, #72260156 |
| maximal normal subgroup of | C3×D5×#805, #72260139, #72260156 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1323);