Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of #6653 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#6653 |
| Hall | C32×C5 ⋊ D8 |
| Sylow | C32 ⋊ D40 |
| Sylow | C5 ⋊ C3×#213 |
104 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6653, #13085672, #13085674, … |
| maximal normal subgroup of | D3×#6653, #13085672, #13085674, … |
| maximal quotient of | C3×#90938, C3×#90942, C3×#90943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 202);