Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of PSU(3,𝔽2)⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | PSU(3,𝔽2)⋊Dic5 |
| Hall | C32×C5 ⋊ #103 |
| Sylow | C32 ⋊ #3967 |
| Sylow | C5 ⋊ PSU(3,𝔽2)⋊C4 |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
Polycyclic presentation:
2^5,3^2,5|a^2=d,b^2=e,c^2=e,b^a=bc,c^a=ce,f^a=f^2,h^a=h^4,c^b=ce,f^b=fg,g^b=fg^2,f^c=g^2,g^c=f,f^e=f^2,g^e=g^242 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4714);