Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×D3×C8 |
| Fitting | C32×C5×C8 ⋊ C2 |
| derived | C3 ⋊ C2×C3×C5×C8 |
| Hall | C32×C5 ⋊ C2×C8 |
| Sylow | C32 ⋊ C2×C5×C8 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×#672, C3×#90935, C5×D3×C3⋊C16, … |
| maximal normal subgroup of | C3×D3×#672, C3×#90935, C5×D3×C3⋊C16, … |
| maximal quotient of | C3×C5×D3×C16, C3×C5×#798, C3×C5×C8×Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 319);