Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C32×C5 ⋊ SD16 |
| Sylow | C32 ⋊ #677 |
| Sylow | C5 ⋊ #3716 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^4,3^2,5|b^2=c,c^2=d,b^a=bc,c^a=cd,f^a=f^2,g^a=g^4,e^b=e^296 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3716, D3×#6657, #13085696, … |
| maximal normal subgroup of | D5×#3716, D3×#6657, #13085696, … |
| maximal quotient of | #13084841, #13084850, #13084863, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 272);