Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C5×C9 ⋊ M16 |
| Sylow | C9 ⋊ #700 |
| Sylow | C5 ⋊ #3663 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^4,3,5,3|a^2=c,b^2=d,c^2=d,e^3=g,b^a=bd,f^a=f^2,e^b=e^2g^2,g^b=g^2,f^c=f^454 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#700, #13085165, #13085167, … |
| maximal normal subgroup of | D9×#700, #13085165, #13085167, … |
| maximal quotient of | Dic9⋊#170, #13083931, #13083933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 98);