GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
#g4 f4 z2 n1 c4% almost decomposable bravais-group 6 % generator 0 1 0 0 0 0 -1 1 0 0 0 0 0 0 0 1 0 0 0 0 -1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 6 % generator 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 6 % generator 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 -1 1 6 % generator 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 6x0 % invariant form 2 -1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6x0 % invariant form 0 0 0 2 -1 0 -1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 6x0 % invariant form 0 0 0 0 0 2 0 0 -1 2 0 0 0 0 0 0 0 0 0 0 0 6x0 % invariant form 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 -1 2 6 % zentr 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 -1 -1 0 1 0 0 1 0 -1 1 0 0 0 1 0 0 6 % zentr 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 -1 0 0 0 0 1 0 -1 0 0 1 0 1 0 0 0 0 1 0 1 6d0 % generator of normalizer 1 6d1 % generator of centralizer -1 -1 1 1 1 1 6 % generator of centralizer -1 0 0 0 0 0 0 -1 0 0 0 0 -1 0 1 0 0 0 0 -1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 6x0 % generator of centralizer 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 6d1 % generator of centralizer 1 1 1 1 -1 -1 2^4 * 3^2 = 144 % order of the group #g6 f4 n1 c8% not almost decomposable bravais-group 6 % generator 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 1 0 0 0 0 -1 -1 0 0 0 0 0 0 0 1 6 % generator 1 -1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 -1 0 0 0 -1 1 1 -1 0 0 1 0 0 0 0 0 0 1 1 0 6 % generator 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 -1 0 0 1 0 -1 1 0 0 0 0 1 0 0 0 0 0 0 1 6 % generator -1 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 1 0 0 0 0 -1 -1 0 0 0 0 0 0 -1 0 6 % generator -1 0 0 0 0 0 -1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 -1 0 6 % generator 0 1 0 0 0 0 -1 1 0 0 0 0 0 0 1 0 0 1 0 0 -1 1 1 -1 0 0 0 -1 0 1 0 0 -1 0 0 0 6x0 % invariant form 2 -1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6x0 % invariant form 0 0 0 1 -2 0 1 -2 0 0 2 -1 0 0 0 1 1 0 0 0 0 6x0 % invariant form 0 0 0 0 0 2 0 0 2 2 0 0 1 1 2 0 0 -1 -1 1 2 6x0 % invariant form 0 0 0 0 0 2 0 0 -1 2 0 0 -2 1 2 0 0 2 -1 -2 2 6d0 % generator of normalizer 1 6d1 % generator of centralizer -1 -1 1 1 1 1 6d0 % generator of centralizer 1 6 % generator of centralizer 1 0 0 0 -1 -1 0 1 1 1 0 -1 0 0 -1 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 6 % generator of centralizer 1 0 0 0 -1 -1 0 1 1 1 0 -1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 6d1 % generator of centralizer 1 1 -1 -1 -1 -1 6 % generator of centralizer 1 0 0 0 1 1 0 1 -1 -1 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 6 % generator of centralizer 2 0 0 0 -1 -1 0 2 1 1 0 -1 1 -2 -1 -2 -1 1 0 0 0 1 0 0 2 -1 -1 -1 -1 -1 1 1 1 1 -1 -1 6d0 % generator of centralizer -1 2^3 * 3^2 = 72 % order of the group #g7 f4 n1 c5% not almost decomposable bravais-group 6 % generator 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 % generator -1 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 1 0 0 0 1 -1 0 0 0 0 1 0 0 0 6 % generator 0 1 0 0 0 0 -1 1 0 0 0 0 0 0 0 1 0 0 0 0 -1 1 0 0 0 0 0 0 0 1 0 0 0 0 -1 1 6 % generator -1 1 0 0 0 0 0 1 0 0 0 0 0 0 -1 1 0 0 0 0 0 1 0 0 0 0 0 0 -1 1 0 0 0 0 0 1 6 % generator 1 -1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 -1 0 0 0 -1 1 0 0 0 0 -1 0 0 0 6 % generator 0 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 % generator -1 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 -1 0 0 1 0 0 0 0 0 1 -1 0 0 6x0 % invariant form 2 -1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6x0 % invariant form 0 0 0 2 -1 0 -1 2 0 0 -2 1 0 0 0 1 -2 0 0 0 0 6x0 % invariant form 0 0 0 0 0 2 0 0 -1 2 0 0 -2 1 2 0 0 1 -2 -1 2 6x0 % invariant form 0 0 0 0 0 2 0 0 -1 2 0 0 2 -1 2 0 0 -1 2 -1 2 6d0 % generator of normalizer 1 6d1 % generator of centralizer -1 -1 1 1 1 1 6 % generator of centralizer 0 0 -1 0 1 0 0 0 0 -1 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 6x0 % generator of centralizer 1 0 1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 0 6d0 % generator of centralizer 1 6 % generator of centralizer 1 0 -1 0 1 0 0 1 0 -1 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 2^3 * 3^1 = 24 % order of the group #g4 f4 z2 % almost decomposable bravais-group 6 % generator 0 1 0 0 0 0 -1 1 0 0 0 0 0 0 0 1 0 0 0 0 -1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 6 % generator 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 6 % generator 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 -1 1 6 % generator 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 6x0 % invariant form 2 -1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6x0 % invariant form 0 0 0 0 0 2 0 0 -1 2 0 0 0 0 0 0 0 0 0 0 0 6x0 % invariant form 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6x0 % invariant form 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 -1 2 6 % zentr 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 -1 -1 0 1 0 0 1 0 -1 1 0 0 0 1 0 0 6 % zentr 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 -1 0 0 0 0 1 0 -1 0 0 1 0 1 0 0 0 0 1 0 1 2^4 * 3^2 = 144 % order of the group #g5 f4 % not almost decomposable bravais-group 6 % generator -1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 6 % generator 1 -1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 -1 0 0 0 -1 1 1 -1 0 0 1 0 0 0 0 0 0 1 1 0 6 % generator 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 -1 0 0 1 0 -1 1 0 0 0 0 1 0 0 0 0 0 0 1 6 % generator -1 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 1 0 0 0 0 -1 -1 0 0 0 0 0 0 -1 0 6 % generator 0 1 0 0 0 0 -1 1 0 0 0 0 0 0 1 0 0 1 0 0 -1 1 1 -1 0 0 0 -1 0 1 0 0 -1 0 0 0 6x0 % invariant form 2 -1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6x0 % invariant form 0 0 0 0 0 2 0 0 2 2 0 0 1 1 2 0 0 -1 -1 1 2 6x0 % invariant form 0 0 0 -1 0 0 -1 0 0 0 0 -1 0 0 0 1 -1 0 0 0 0 6x0 % invariant form 0 0 0 0 0 2 0 0 -1 2 0 0 -2 1 2 0 0 2 -1 -2 2 2^3 * 3^2 = 72 % order of the group #g7 f4 % not almost decomposable bravais-group 6 % generator 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 % generator -1 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 1 0 0 0 1 -1 0 0 0 0 1 0 0 0 6 % generator 0 1 0 0 0 0 -1 1 0 0 0 0 0 0 0 1 0 0 0 0 -1 1 0 0 0 0 0 0 0 1 0 0 0 0 -1 1 6 % generator -1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 1 0 0 -1 1 0 0 0 0 0 1 0 0 6 % generator 1 -1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 -1 0 0 0 -1 1 0 0 0 0 -1 0 0 0 6 % generator 0 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 % generator -1 0 0 0 0 0 -1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 -1 0 0 0 0 0 0 1 0 0 0 0 0 1 -1 6x0 % invariant form 2 -1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6x0 % invariant form 0 0 0 0 0 2 0 0 -1 2 0 0 -2 1 2 0 0 1 -2 -1 2 6x0 % invariant form 0 0 0 0 -1 0 1 0 0 0 0 1 0 0 0 -1 0 0 0 0 0 6x0 % invariant form 0 0 0 0 0 2 0 0 -1 2 0 0 2 -1 2 0 0 -1 2 -1 2 2^3 * 3^1 = 24 % order of the group