Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C2×C32×Dic10 |
| unambiguous semidirect product | (C2×C5)⋊(C32×Q8) |
| Hall | C32×C5 ⋊ C2×Q8 |
| Sylow | C5 ⋊ C2×C32×Q8 |
228 conjugacy classes of subgroups.
| transitive degree | μt(G) = 720 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#90961, C3×#90970, C3×#90971, … |
| maximal normal subgroup of | C3×#90961, C3×#90970, C3×#90971, … |
| maximal quotient of | C32×C4×Dic10, C32×#4015, C32×#4016, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 709);