Example

gap> R1 := GroupAssociationScheme(SymmetricGroup(4));;
gap> T1 := CharacterTableOfAssociationScheme(R1);;
gap> Display(T1);
[ [   1,   6,   3,   8,   6,   1 ],
  [   1,  -6,   3,   8,  -6,   1 ],
  [   1,   0,   3,  -4,   0,   4 ],
  [   1,  -2,  -1,   0,   2,   9 ],
  [   1,   2,  -1,   0,  -2,   9 ] ]
gap> IsCharacterTableAS(R1, T1);
true
gap> FrameQuotient(T1);
36864
gap> FrameNumber(T1);  
21233664
gap> FactorsInt(last);
[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3 ]
gap> R2 := CyclotomicScheme(5, 2);;
gap> CharacterTableOfAssociationScheme(R2);
false
gap> Display(CharacterTableOfAssociationScheme(R2, CF(5)));
[ [              1,              2,              2,              1 ],
  [              1,  E(5)^2+E(5)^3,    E(5)+E(5)^4,              2 ],
  [              1,    E(5)+E(5)^4,  E(5)^2+E(5)^3,              2 ] ]
gap> G := SymmetricGroup(5);;
gap> H := Subgroup(G, [(1,2,3,4)]);;
gap> R3 := SchurianScheme(G, H);;                 
gap> T3 := CharacterTableOfAssociationScheme(R3);;
gap> Display(T3);
[ [   1,   1,   4,   4,   4,   4,   4,   4,   4,   1 ],
  [   2,   0,  -2,  -2,  -2,   3,  -1,   3,  -1,   5 ],
  [   1,  -1,   0,  -3,   3,  -1,   1,  -1,   1,   4 ],
  [   1,   1,   4,  -1,  -1,  -1,  -1,  -1,  -1,   4 ],
  [   1,   1,  -2,   2,   2,  -1,  -1,  -1,  -1,   5 ],
  [   1,  -1,   0,   2,  -2,  -1,   1,  -1,   1,   6 ] ]
gap> FrameNumber(T3);
1074954240000