Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #6758 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C2×C4 |
| direct product | C3×#91989 |
| Fitting | C2×C32×C4×C5 ⋊ C4 |
| Hall | C32×C5 ⋊ #117 |
| Sylow | C32 ⋊ #4130 |
| Sylow | C5 ⋊ C3×#926 |
358 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11756987, C3×#11756836, #72230215, … |
| maximal normal subgroup of | C3×#11756987, C3×#11756836, #72230215, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5458);