Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of #1201 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#6665 |
| Hall | C32×C5 ⋊ C22⋊C4 |
| Sylow | C32 ⋊ #685 |
| Sylow | C5 ⋊ C3×#217 |
168 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6665, #13085856, #13085862, … |
| maximal normal subgroup of | D3×#6665, #13085856, #13085862, … |
| maximal quotient of | C3×#90955, C3×#90958, C3×#90961, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 214);