Set of generators: 8 Groups: 5 Vector spaces (start): 406 Vector spaces (end): 36 (100, 10, '(C5 x C5) : C4') Vector space of dimension 0 with basis: (1, 1, '1') Vector space of dimension 8 with basis: [1, 0, 0, 0, 0, 0, 0, 0] [0, 1, 0, 0, 0, 0, 0, 0] [0, 0, 1, 0, 0, 0, 0, 0] [0, 0, 0, 1, 0, 0, 0, 0] [0, 0, 0, 0, 1, 0, 0, 0] [0, 0, 0, 0, 0, 1, 0, 0] [0, 0, 0, 0, 0, 0, 1, 0] [0, 0, 0, 0, 0, 0, 0, 1] (2, 1, 'C2') Vector space of dimension 4 with basis: [0, exp(6*pi*I/5), 1, 0, 0, 0, 0, 0] [exp(2*pi*I/5), 0, 0, 1, 0, 0, 0, 0] [0, 0, 0, 0, 0, exp(2*pi*I/5), 1, 0] [0, 0, 0, 0, exp(4*pi*I/5), 0, 0, 1] Vector space of dimension 4 with basis: [0, 1, 1, 0, 0, 0, 0, 0] [1, 0, 0, 1, 0, 0, 0, 0] [0, 0, 0, 0, 0, 1, 1, 0] [0, 0, 0, 0, 1, 0, 0, 1] Vector space of dimension 4 with basis: [0, exp(8*pi*I/5), 1, 0, 0, 0, 0, 0] [exp(6*pi*I/5), 0, 0, 1, 0, 0, 0, 0] [0, 0, 0, 0, 0, exp(6*pi*I/5), 1, 0] [0, 0, 0, 0, exp(2*pi*I/5), 0, 0, 1] Vector space of dimension 4 with basis: [0, exp(2*pi*I/5), 1, 0, 0, 0, 0, 0] [exp(4*pi*I/5), 0, 0, 1, 0, 0, 0, 0] [0, 0, 0, 0, 0, exp(4*pi*I/5), 1, 0] [0, 0, 0, 0, exp(8*pi*I/5), 0, 0, 1] Vector space of dimension 4 with basis: [0, exp(4*pi*I/5), 1, 0, 0, 0, 0, 0] [exp(8*pi*I/5), 0, 0, 1, 0, 0, 0, 0] [0, 0, 0, 0, 0, exp(8*pi*I/5), 1, 0] [0, 0, 0, 0, exp(6*pi*I/5), 0, 0, 1] (5, 1, 'C5') Vector space of dimension 2 with basis: [1, 0, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 1, 0, 0, 0] Vector space of dimension 2 with basis: [0, 0, 1, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 1, 0] Vector space of dimension 2 with basis: [0, 1, 0, 0, 0, 0, 0, 0] [0, 0, 0, 0, 0, 1, 0, 0] Vector space of dimension 2 with basis: [0, 0, 0, 1, 0, 0, 0, 0] [0, 0, 0, 0, 0, 0, 0, 1] (4, 1, 'C4') Vector space of dimension 2 with basis: [exp(8*pi*I/5), exp(4*pi*I/5), 1, 1, 0, 0, 0, 0] [0, 0, 0, 0, exp(6*pi*I/5), exp(8*pi*I/5), 1, 1] Vector space of dimension 2 with basis: [exp(2*pi*I/5), exp(6*pi*I/5), 1, 1, 0, 0, 0, 0] [0, 0, 0, 0, exp(4*pi*I/5), exp(2*pi*I/5), 1, 1] Vector space of dimension 2 with basis: [exp(4*pi*I/5), 1, exp(8*pi*I/5), 1, 0, 0, 0, 0] [0, 0, 0, 0, exp(8*pi*I/5), 1, exp(6*pi*I/5), 1] Vector space of dimension 2 with basis: [exp(4*pi*I/5), exp(8*pi*I/5), exp(6*pi*I/5), 1, 0, 0, 0, 0] [0, 0, 0, 0, exp(8*pi*I/5), exp(6*pi*I/5), exp(2*pi*I/5), 1] Vector space of dimension 2 with basis: [exp(6*pi*I/5), exp(2*pi*I/5), exp(4*pi*I/5), 1, 0, 0, 0, 0] [0, 0, 0, 0, exp(2*pi*I/5), exp(4*pi*I/5), exp(8*pi*I/5), 1] Vector space of dimension 2 with basis: [exp(8*pi*I/5), exp(2*pi*I/5), exp(8*pi*I/5), 1, 0, 0, 0, 0] [0, 0, 0, 0, exp(6*pi*I/5), exp(4*pi*I/5), exp(6*pi*I/5), 1] Vector space of dimension 2 with basis: [exp(8*pi*I/5), 1, exp(6*pi*I/5), 1, 0, 0, 0, 0] [0, 0, 0, 0, exp(6*pi*I/5), 1, exp(2*pi*I/5), 1] Vector space of dimension 2 with basis: [exp(6*pi*I/5), exp(8*pi*I/5), 1, 1, 0, 0, 0, 0] [0, 0, 0, 0, exp(2*pi*I/5), exp(6*pi*I/5), 1, 1] Vector space of dimension 2 with basis: [exp(2*pi*I/5), 1, exp(4*pi*I/5), 1, 0, 0, 0, 0] [0, 0, 0, 0, exp(4*pi*I/5), 1, exp(8*pi*I/5), 1] Vector space of dimension 2 with basis: [1, exp(6*pi*I/5), exp(6*pi*I/5), 1, 0, 0, 0, 0] [0, 0, 0, 0, 1, exp(2*pi*I/5), exp(2*pi*I/5), 1] Vector space of dimension 2 with basis: [exp(6*pi*I/5), 1, exp(2*pi*I/5), 1, 0, 0, 0, 0] [0, 0, 0, 0, exp(2*pi*I/5), 1, exp(4*pi*I/5), 1] Vector space of dimension 2 with basis: [exp(6*pi*I/5), exp(4*pi*I/5), exp(6*pi*I/5), 1, 0, 0, 0, 0] [0, 0, 0, 0, exp(2*pi*I/5), exp(8*pi*I/5), exp(2*pi*I/5), 1] Vector space of dimension 2 with basis: [1, exp(4*pi*I/5), exp(4*pi*I/5), 1, 0, 0, 0, 0] [0, 0, 0, 0, 1, exp(8*pi*I/5), exp(8*pi*I/5), 1] Vector space of dimension 2 with basis: [exp(2*pi*I/5), exp(8*pi*I/5), exp(2*pi*I/5), 1, 0, 0, 0, 0] [0, 0, 0, 0, exp(4*pi*I/5), exp(6*pi*I/5), exp(4*pi*I/5), 1] Vector space of dimension 2 with basis: [exp(8*pi*I/5), exp(8*pi*I/5), exp(4*pi*I/5), 1, 0, 0, 0, 0] [0, 0, 0, 0, exp(6*pi*I/5), exp(6*pi*I/5), exp(8*pi*I/5), 1] Vector space of dimension 2 with basis: [exp(4*pi*I/5), exp(4*pi*I/5), exp(2*pi*I/5), 1, 0, 0, 0, 0] [0, 0, 0, 0, exp(8*pi*I/5), exp(8*pi*I/5), exp(4*pi*I/5), 1] Vector space of dimension 2 with basis: [exp(4*pi*I/5), exp(2*pi*I/5), 1, 1, 0, 0, 0, 0] [0, 0, 0, 0, exp(8*pi*I/5), exp(4*pi*I/5), 1, 1] Vector space of dimension 2 with basis: [exp(4*pi*I/5), exp(6*pi*I/5), exp(4*pi*I/5), 1, 0, 0, 0, 0] [0, 0, 0, 0, exp(8*pi*I/5), exp(2*pi*I/5), exp(8*pi*I/5), 1] Vector space of dimension 2 with basis: [exp(8*pi*I/5), exp(6*pi*I/5), exp(2*pi*I/5), 1, 0, 0, 0, 0] [0, 0, 0, 0, exp(6*pi*I/5), exp(2*pi*I/5), exp(4*pi*I/5), 1] Vector space of dimension 2 with basis: [1, 1, 1, 1, 0, 0, 0, 0] [0, 0, 0, 0, 1, 1, 1, 1] Vector space of dimension 2 with basis: [exp(6*pi*I/5), exp(6*pi*I/5), exp(8*pi*I/5), 1, 0, 0, 0, 0] [0, 0, 0, 0, exp(2*pi*I/5), exp(2*pi*I/5), exp(6*pi*I/5), 1] Vector space of dimension 2 with basis: [1, exp(8*pi*I/5), exp(8*pi*I/5), 1, 0, 0, 0, 0] [0, 0, 0, 0, 1, exp(6*pi*I/5), exp(6*pi*I/5), 1] Vector space of dimension 2 with basis: [exp(2*pi*I/5), exp(2*pi*I/5), exp(6*pi*I/5), 1, 0, 0, 0, 0] [0, 0, 0, 0, exp(4*pi*I/5), exp(4*pi*I/5), exp(2*pi*I/5), 1] Vector space of dimension 2 with basis: [exp(2*pi*I/5), exp(4*pi*I/5), exp(8*pi*I/5), 1, 0, 0, 0, 0] [0, 0, 0, 0, exp(4*pi*I/5), exp(8*pi*I/5), exp(6*pi*I/5), 1] Vector space of dimension 2 with basis: [1, exp(2*pi*I/5), exp(2*pi*I/5), 1, 0, 0, 0, 0] [0, 0, 0, 0, 1, exp(4*pi*I/5), exp(4*pi*I/5), 1] Resume: groups: 5 group (1, 1, '1') with 1 components, of which 1 of dimension 8 group (2, 1, 'C2') with 5 components, of which 5 of dimension 4 group (4, 1, 'C4') with 25 components, of which 25 of dimension 2 group (5, 1, 'C5') with 4 components, of which 4 of dimension 2 group (100, 10, '(C5 x C5) : C4') with 1 components, of which 1 of dimension 0