Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C9⋊#168) |
| Hall | C5×C9 ⋊ C4⋊C8 |
| Sylow | C9 ⋊ C4⋊#168 |
| Sylow | C5 ⋊ C4⋊(C9⋊C8) |
114 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1440 |
Polycyclic presentation:
2^5,3,5,3|a^2=d,b^2=c,d^2=e,f^3=h,b^a=bc,f^a=f^2h^2,g^a=g^4,h^a=h^2372 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 164);