Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×#216 |
| Hall | C32×C5 ⋊ Q16 |
| Sylow | C32 ⋊ C5×Q16 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#216, C3×#91508, C3×#91511, … |
| maximal normal subgroup of | C3×D5×#216, C3×#91508, C3×#91511, … |
| maximal quotient of | C3×C5×#807, C3×C5×#810, C3×C5×#835, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 333);