Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D9×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | (C9⋊AGL(1,𝔽5))⋊C8 |
| derived, Hall | C5×C9 ⋊ C4×C8 |
| Sylow | C9 ⋊ C8×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C8×Dic9 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
Polycyclic presentation:
2^5,3,5,3|a^2=c,b^2=d,c^2=e,d^2=e,f^3=h,g^a=g^2,f^b=f^2h^2,h^b=h^2,g^c=g^4120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 235);