Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×C5×D3×Q8 |
| Fitting | C32×C5×Q8 ⋊ C2 |
| Hall | C32×C5 ⋊ C2×Q8 |
| Sylow | C32 ⋊ C2×C5×Q8 |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#688, C3×D3×#689, C3×#91518, … |
| maximal normal subgroup of | C3×D3×#688, C3×D3×#689, C3×#91518, … |
| maximal quotient of | C3×C5×#887, C3×C5×#896, C3×C5×#888, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 725);