Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C5×C9 ⋊ SD16 |
| Sylow | C9 ⋊ #688 |
| Sylow | C5 ⋊ #3664 |
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=bcd,f^a=f^4,c^b=cd,e^b=e^2g^2,g^b=g^281 conjugacy classes — view the full character table.
| maximal subgroup of | #13084004, D5×#3664, #13084011, … |
| maximal normal subgroup of | #13084004, D5×#3664, #13084011, … |
| maximal quotient of | #13083727, #13083729, #13083735, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 12);