Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×#213 |
| Fitting | C32×C5×D4 ⋊ C2 |
| Hall | C32×C5 ⋊ D8 |
| Sylow | C32 ⋊ C5×D8 |
104 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#213, C3×#91478, C3×#91481, … |
| maximal normal subgroup of | C3×D5×#213, C3×#91478, C3×#91481, … |
| maximal quotient of | C3×C5×#807, C3×C5×#809, C3×C5×#826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 330);