Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of Dic30 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×C3×Dic30 |
| Hall | C32×C5 ⋊ C2×Q8 |
| Sylow | C32 ⋊ C2×Dic10 |
| Sylow | C5 ⋊ C2×C3×Dic6 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#90963, C3×#90974, C3×#90975, … |
| maximal normal subgroup of | C3×#90963, C3×#90974, C3×#90975, … |
| maximal quotient of | C3×C4×Dic30, C3×#91758, C3×#91759, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 729);