Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C5×C8×C9 ⋊ C2 |
| Hall | C5×C9 ⋊ M16 |
| Sylow | C9 ⋊ #676 |
| 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|b^2=c,c^2=d,e^3=g,b^a=bd,e^a=e^2g^2,f^a=f^4,g^a=g^2186 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3663, D9×#676, #13084014, … |
| maximal normal subgroup of | D5×#3663, D9×#676, #13084014, … |
| maximal quotient of | #13083858, #13083859, #13083863, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 67);