Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Hall | C32×C5 ⋊ M32 |
| Sylow | C32 ⋊ #3944 |
| Sylow | C5 ⋊ #63639 |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 720 |
Polycyclic presentation:
2^5,3^2,5|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^2,g^a=g^2,h^a=h^4372 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1412);