Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C3⋊ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊#3928) |
| derived, Hall | C32×C5 ⋊ C32 |
| Sylow | C32 ⋊ #3928 |
| Sylow | C5 ⋊ C3⋊(C3⋊C32) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | C3⋊ΓL(1,𝔽16) |
| commutator, hypocenter | C32×C5 | C32 |
| Fitting | C32×C5×C8 | C4 |
| socle, prime radical | C2×C32×C5 | C16 |
| cosocle | C32×#672 | C2 |
| LCS | G ▷ C32×C5 | |
| UCS | C1 ◁ C8 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1440 |
Polycyclic presentation:
2^5,3^2,5|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^2,g^a=g^2,h^a=h^2,h^b=h^4168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 945);