Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×#237 |
| Fitting | C32×C5×D4 ⋊ C2 |
| Hall | C32×C5 ⋊ #41 |
| Sylow | C32 ⋊ C5×#41 |
176 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#91480, C3×#91486, C3×#91493, … |
| maximal normal subgroup of | C3×#91480, C3×#91486, C3×#91493, … |
| maximal quotient of | C3×C5×#877, C3×C5×#878, C3×C5×#885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 724);