Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of #625 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#3712 |
| Hall | C32×C5 ⋊ M16 |
| Sylow | C32 ⋊ C5×M16 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#63727, C5×#63728, C5×#63731, … |
| maximal normal subgroup of | C5×#63727, C5×#63728, C5×#63731, … |
| maximal quotient of | C5×#63555, C5×#63557, C5×#63572, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 248);