Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of D3×D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C3×D3×#168 |
| derived | C3×C5 ⋊ C2×C3×C8 |
| Hall | C32×C5 ⋊ C2×C8 |
| Sylow | C32 ⋊ C2×#168 |
| Sylow | C5 ⋊ C3×D3×C8 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#674, C3×#91165, D3×C3⋊#674, … |
| maximal normal subgroup of | C3×D3×#674, C3×#91165, D3×C3⋊#674, … |
| maximal quotient of | C3×D3×#672, C3×#90935, C3×Dic3×#168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 196);