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I am trying to construct in MAGMA the group $PSL(2, 81)⋊(Z_4 × Z_2)$ I can't make homomorphism from $(Z_4 × Z_2)$ to $Aut(PSL(2, 81))$. I tried the following

G:=PSL(2, 81);
A:=AutomorphismGroup(G);
K1:=CyclicGroup(4);
K2:=CyclicGroup(2);
H:=DirectProduct(K1, K2);
phi:=hom< H-> A|<H.1, A.3>, <H.2, A.2>>;
S:=SemidirectProduct(G, H, phi);
S;

but I get the following output

 SemidirectProduct(

 K: GrpPerm: K, Degree 21, Order 2^6 * 3^2 * 5 * 7,
 H: GrpPerm: H, Degree 6, Order 2^3,
 phi: Homomorphism of GrpPerm: H, Degree 6, Order 2^3 into A group...
 )
 In file "/magSemidirectProduct(
 K: GrpPerm: K, Degree 82, Order 2^4 * 3^4 * 5 * 41,
 H: GrpPerm: H, Degree 6, Order 2^3,
 phi: Homomorphism of GrpPerm: H, Degree 6, Order 2^3 into A group...
 )
 In file "/magma/package/Group/GrpFin/semidirect_product.m", line 130, column 35:
 faithful := #sub< P | I, Image(pr) > eq #I * #H;
                                 ^
Runtime error in 'Image': Not a homomorphism: image, kernel, domain orders
incompatible

Can someone help me seeing the error and guid me, how I can compute this semidirectproduct?

user407524
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M.A
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  • Try a simpler semidirect product, and check the orders of the elements you are mapping to – reuns Apr 23 '17 at 08:49
  • Can you say mathematically where you've tried to map the generators of the two cyclic groups? – ancient mathematician Apr 25 '17 at 08:25

0 Answers0