Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C9⋊AGL(1,𝔽5)) |
| Fitting | C4×C5×C9 ⋊ C4 |
| Hall | C5×C9 ⋊ C4⋊C4 |
| Sylow | C9 ⋊ C4⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4⋊Dic9 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
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^3,g^a=g^2,f^c=f^478 conjugacy classes — view the full character table.
| maximal subgroup of | #13083914, #13083915, #13083920, … |
| maximal normal subgroup of | #13083914, #13083915, #13083920, … |
| maximal quotient of | #13083979, #13083980, #13083983, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 121);