Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D9)⋊Dic5 |
| Hall | C5×C9 ⋊ C22⋊C4 |
| Sylow | C9 ⋊ C22⋊Dic5 |
| Sylow | C5 ⋊ (C2×D9)⋊C4 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^4,3,5,3|a^2=c,e^3=g,b^a=bd,f^a=f^4,e^b=e^2g^2,g^b=g^290 conjugacy classes — view the full character table.
| maximal subgroup of | #13084072, #13084075, #13084077, … |
| maximal normal subgroup of | #13084072, #13084075, #13084077, … |
| maximal quotient of | #13083711, #13083717, #13083719, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 29);