Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C5×C9 ⋊ C4⋊Q8 |
| Sylow | C9 ⋊ #4015 |
| Sylow | C5 ⋊ #63431 |
204 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1440 |
Polycyclic presentation:
2^5,3,5,3|a^2=e,b^2=e,c^2=d,f^3=h,b^a=be,c^a=cd,f^a=f^2h^2,g^a=g^4,h^a=h^2366 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 834);