Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D45⋊Q8 |
| Hall | C5×C9 ⋊ C2×Q8 |
| Sylow | C9 ⋊ Q8×D5 |
| Sylow | C5 ⋊ Q8×D9 |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^4,3,5,3|a^2=d,b^2=d,c^2=d,e^3=g,c^a=cd,f^a=f^4,c^b=cd,e^b=e^2g^2,g^b=g^272 conjugacy classes — view the full character table.
| maximal subgroup of | #13084024, #13084032, #13084036, … |
| maximal normal subgroup of | #13084024, #13084032, #13084036, … |
| maximal quotient of | #13084065, #13084070, #13084073, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 128);