Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22×C5×C9 ⋊ C4 |
| Hall | C5×C9 ⋊ C22⋊C4 |
| Sylow | C9 ⋊ C22⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ #3676 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
Polycyclic presentation:
2^4,3,5,3|a^2=c,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 | #13083926, #13083927, #13083993, … |
| maximal normal subgroup of | #13083926, #13083927, #13083993, … |
| maximal quotient of | #13083989, #13083992, #13083993, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 124);