Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#6779 |
| Hall | C32×C5 ⋊ #41 |
| Sylow | C32 ⋊ #709 |
| Sylow | C5 ⋊ C3×#237 |
176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 120 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6779, #13088975, #13088978, … |
| maximal normal subgroup of | D3×#6779, #13088975, #13088978, … |
| maximal quotient of | C3×#91335, C3×#91336, C3×#91337, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 604);