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 ⋊ #676 |
| Sylow | C5 ⋊ #3667 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^4,3,5,3|b^2=c,c^2=d,e^3=g,b^a=bd,f^a=f^4,e^b=e^2g^2,g^b=g^290 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#676, #13084008, #13084013, … |
| maximal normal subgroup of | D9×#676, #13084008, #13084013, … |
| maximal quotient of | #13083709, #13083710, #13083744, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 16);