Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of #6715 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#6715 |
| Fitting | C32×C5×D4 ⋊ C2 |
| Hall | C32×C5 ⋊ D8 |
| Sylow | C32 ⋊ #686 |
| Sylow | C5 ⋊ C3×#213 |
104 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 38 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 | C3×D5×#213, C3×#91478, C3×D3×#686, … |
| maximal normal subgroup of | C3×D5×#213, C3×#91478, C3×D3×#686, … |
| maximal quotient of | C3×#91091, C3×#91093, C3×#91110, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 346);