Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Hall | C32×C5 ⋊ C2×Q8 |
| Sylow | C32 ⋊ Q8×D5 |
| Sylow | C5 ⋊ Q8×C3⋊D3 |
228 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^4,3^2,5|a^2=d,b^2=d,c^2=d,c^a=cd,g^a=g^4,c^b=cd,e^b=e^2,f^b=f^272 conjugacy classes — view the full character table.
| maximal subgroup of | #13085532, #13085694, #13085711, … |
| maximal normal subgroup of | #13085532, #13085694, #13085711, … |
| maximal quotient of | #13086765, #13086770, #13086773, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 622);