Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C9⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#3928 |
| derived, Hall | C5×C9 ⋊ C32 |
| Sylow | C9 ⋊ #3928 |
| Sylow | C5 ⋊ C9⋊C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | C9⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C9 | C32 |
| Frattini | C3×C8 | ΓL(1,𝔽16) |
| Fitting | C5×C8×C9 | C4 |
| socle, prime radical | C2×C3×C5 | C3⋊C16 |
| cosocle | C9×#672 | C2 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C8 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 1440 |
Polycyclic presentation:
2^5,3,5,3|a^2=b,b^2=c,c^2=d,d^2=e,f^3=h,f^a=f^2h^2,g^a=g^2,h^a=h^2,g^b=g^4168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 6);