Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C5×C9 ⋊ Q32 |
| Sylow | C9 ⋊ #3961 |
| Sylow | C5 ⋊ #63388 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 1440 |
Polycyclic presentation:
2^5,3,5,3|a^2=e,b^2=e,c^2=de,d^2=e,f^3=h,b^a=bc,c^a=cd,d^a=de,g^a=g^4,c^b=cd,d^b=de,f^b=f^2h^2,h^b=h^2117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 23);