Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C9⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D5⋊(C9⋊C16) |
| derived, Hall | C5×C9 ⋊ C2×C16 |
| Sylow | C9 ⋊ D5⋊C16 |
| Sylow | C5 ⋊ C2×C9⋊C16 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 720 |
Polycyclic presentation:
2^5,3,5,3|a^2=c,b^2=d,c^2=d,d^2=e,f^3=h,f^a=f^2h^2,g^a=g^2,h^a=h^2,g^c=g^4168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 294);