Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×#204 |
| Fitting | C32×C5×C8 ⋊ C2 |
| Hall | C32×C5 ⋊ SD16 |
| Sylow | C32 ⋊ C5×SD16 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×#204, C3×#91249, C3×#91255, … |
| maximal normal subgroup of | C3×D5×#204, C3×#91249, C3×#91255, … |
| maximal quotient of | C3×C5×#817, C3×C5×#821, C3×C5×#816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 321);