Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊Dic45 |
| Hall | C5×C9 ⋊ C4⋊C4 |
| Sylow | C9 ⋊ C4⋊Dic5 |
| Sylow | C5 ⋊ C4⋊Dic9 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 720 |
Polycyclic presentation:
2^4,3,5,3|a^2=c,b^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 | #13083714, #13083716, #13083727, … |
| maximal normal subgroup of | #13083714, #13083716, #13083727, … |
| maximal quotient of | C4⋊(C9⋊#168), #13083856, #13083860, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 74);