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×#3711 |
| Hall | C32×C5 ⋊ M16 |
| Sylow | C32 ⋊ C5×M16 |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3711, #13085640, #13085647, … |
| maximal normal subgroup of | D5×#3711, #13085640, #13085647, … |
| maximal quotient of | C5×#63554, C5×(C2×D3)⋊(C3⋊C8), C5×Dic3⋊(C3⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 247);