Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#10624236 |
| Fitting | C23×C32×C5 ⋊ C22 |
| Hall | C32×C5 ⋊ C22×D4 |
| Sylow | C32 ⋊ C22×C22⋊D5 |
| Sylow | C5 ⋊ C2×#3811 |
1078 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D5×#3811, C2×#72231392, #72259868, … |
| maximal normal subgroup of | C2×D5×#3811, #72259868, #72259900 |
| maximal quotient of | #72230429, C2×#72231392 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5749);