Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of Dic30 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | C3×C4⋊Dic15 |
| unambiguous semidirect product | C4⋊(C3×Dic15) |
| Hall | C32×C5 ⋊ C4⋊C4 |
| Sylow | C32 ⋊ C4⋊Dic5 |
| Sylow | C5 ⋊ C3×C4⋊Dic3 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#90965, C3×#90967, C3×#90971, … |
| maximal normal subgroup of | C3×#90965, C3×#90967, C3×#90971, … |
| maximal quotient of | C3×C4⋊(C3⋊#168), C3×#91101, C3×#91102, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 344);