Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of #3714 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#3716 |
| Hall | C32×C5 ⋊ SD16 |
| Sylow | C32 ⋊ C5×SD16 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3716, #13085689, #13085694, … |
| maximal normal subgroup of | D5×#3716, #13085689, #13085694, … |
| maximal quotient of | C5×#63563, C5×#63567, C5×#63573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 252);