Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C5×C9 ⋊ C22⋊C4 |
| Sylow | C9 ⋊ #685 |
| 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,b^2=cd,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 | #13084071, #13084079, #13084080, … |
| maximal normal subgroup of | #13084071, #13084079, #13084080, … |
| maximal quotient of | #13083712, #13083718, #13083720, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 30);