Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | C3×D3×#170 |
| derived | C3×C5 ⋊ C2×C3×C8 |
| Hall | C32×C5 ⋊ C2×C8 |
| Sylow | C32 ⋊ C2×#170 |
| Sylow | C5 ⋊ C3×D3×C8 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#170, D3×#6738, D3×#6739, … |
| maximal normal subgroup of | D32×#170, D3×#6738, D3×#6739, … |
| maximal quotient of | C3×D3×#674, C3×#91165, C3×Dic3×#170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 428);