Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C5×C9 ⋊ Q16 |
| Sylow | C9 ⋊ #689 |
| Sylow | C5 ⋊ #3674 |
54 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 720 |
Polycyclic presentation:
2^4,3,5,3|a^2=d,b^2=d,c^2=d,e^3=g,b^a=bc,c^a=cd,e^a=e^2g^2,f^a=f^4,g^a=g^2,c^b=cd117 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3674, #13084261, #13084264, … |
| maximal normal subgroup of | D5×#3674, #13084261, #13084264, … |
| maximal quotient of | #13083850, #13083852, #13083879, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 78);