Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Hall | C32×C5 ⋊ Q16 |
| Sylow | C32 ⋊ #689 |
| Sylow | C5 ⋊ #3756 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 720 |
Polycyclic presentation:
2^4,3^2,5|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=f^2,g^a=g^4,c^b=cd117 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3756, #13086991, C3⋊D3×#689, … |
| maximal normal subgroup of | D5×#3756, #13086991, C3⋊D3×#689, … |
| maximal quotient of | #13085090, #13085093, #13085118, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 381);