Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of #1201 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#6650 |
| Hall | C32×C5 ⋊ M16 |
| Sylow | C32 ⋊ #681 |
| Sylow | C5 ⋊ C3×ΓL(1,𝔽25) |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6650, #13085645, #13085647, … |
| maximal normal subgroup of | D3×#6650, #13085645, #13085647, … |
| maximal quotient of | C3×#90953, C3×(C2×D3)⋊#168, C3×Dic3⋊#168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 199);