Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×D3×C22⋊D5 |
| Fitting | C22×C32×C5 ⋊ C22 |
| Hall | C32×C5 ⋊ C2×D4 |
| Sylow | C32 ⋊ C2×C22⋊D5 |
| Sylow | C5 ⋊ C3×D3×D4 |
232 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6779, D3×#6780, #13088989, … |
| maximal normal subgroup of | D3×#6779, D3×#6780, #13088989, … |
| maximal quotient of | C3×D3×#683, C3×#91416, C3×#91421, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 614);