Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of #3774 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#3775 |
| Hall | C32×C5 ⋊ SD16 |
| Sylow | C32 ⋊ C5×SD16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
75 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3775, #13088463, #13088467, … |
| maximal normal subgroup of | D5×#3775, #13088463, #13088467, … |
| maximal quotient of | C5×#63739, C5×#63740, C5×#63742, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 470);