Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#92049 |
| Fitting | C23×C32×C5 ⋊ C22 |
| Hall | C32×C5 ⋊ H(5,𝔽2) |
| Sylow | C32 ⋊ #4144 |
| Sylow | C5 ⋊ C3×#1004 |
718 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#1004, #72259900, #72259929 |
| maximal normal subgroup of | C3×D5×#1004, #72259900, #72259929 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5570);