Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C5×C9 ⋊ C4⋊C4 |
| Sylow | C9 ⋊ #683 |
| Sylow | C5 ⋊ Dic9⋊C4 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 720 |
Polycyclic presentation:
2^4,3,5,3|a^2=d,b^2=c,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 | #13084069, #13084070, #13084073, … |
| maximal normal subgroup of | #13084069, #13084070, #13084073, … |
| maximal quotient of | #13083850, #13083851, #13083858, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 73);