Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C4×C5×C9 ⋊ C22 |
| Hall | C5×C9 ⋊ C2×#41 |
| Sylow | C9 ⋊ D5×#41 |
| Sylow | C5 ⋊ #41×D9 |
492 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^5,3,5,3|c^2=e,f^3=h,d^a=de,g^a=g^4,d^b=de,f^b=f^2h^2,h^b=h^2144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1588);