Is it possible to find the structure description of the Jacobson radical $J(FG)$ of a group algebra FG, where F and G are finite field and group respectively in GAP?
I choose the group algebra $F_3D_{30}$, where $F$ is a finite field of characteristic $3$ and $D_{30}$ is the dihedral group of order $30.$ Actually I need the algebraic structure of $1+J(F_3D_{30})$ as it is a subgroup of the unit group $U(F_3D_{30})$, so I am thinking first the structure of $J(F_3D_{30})$. I tried as
gap> RadicalOfAlgebra(GroupRing(GF(3),D30));
<algebra of dimension 20 over GF(3)>
gap> H:=RadicalOfAlgebra(GroupRing(GF(3),D30));;
gap> Size(H);
3486784401
gap> IsAbelian(H);
false
gap> Center(H);
<algebra of dimension 10 over GF(3)>
brk_3> StructureDescription(H);
Error, no method found!
StructureDescription is not working. Is there any way to find its algebraic structure using GAP? Please help. Thank you.