Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#10624218 |
| Fitting | C23×C32×C5 ⋊ C22 |
| Hall | C32×C5 ⋊ C22×D4 |
| Sylow | C32 ⋊ C2×D4×D5 |
| Sylow | C5 ⋊ C2×#3811 |
1078 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D5×#3811, #72231742, C2×#72231387, … |
| maximal normal subgroup of | C2×D5×#3811, #72231742, #72259929 |
| maximal quotient of | #72230423, C2×#72231387 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5712);