Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C32×C5×C8 ⋊ C2 |
| Hall | C32×C5 ⋊ D8 |
| Sylow | C32 ⋊ D40 |
| Sylow | C5 ⋊ #3745 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^4,3^2,5|b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^2,g^a=g^4183 conjugacy classes — view the full character table.
| maximal subgroup of | #13084706, #13084707, #13084711, … |
| maximal normal subgroup of | #13084706, #13084707, #13084711, … |
| maximal quotient of | #13085082, #13085083, #13085084, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 370);