Permutation Representations

Points ID Prim Trans Rank Suborbits Char Stab Files
27 Primitive 1 3 1, 10, 16 24:A5 m b g M view
36 Primitive 1 3 1, 15, 20 S6 m b g M view
40 a Primitive 1 3 1, 12, 27 31+2:2A4 m b g M view
40 b Primitive 1 3 1, 12, 27 33:S4 m b g M view
45 Primitive 1 3 1, 12, 32 2.(A4 × A4).2 m b g M view

Matrix Representations

Char Ring Dim ID Ind Character Char Rng H1 H2 Schur Irr Files
0 Z[ω] 5 a o χ2 Z[ω] 1 Abs irr m b g M view
0 Z[ω] 5 a o χ2 Z[ω] 1 Abs irr m b g M view
0 Z[ω] 5 a o χ2 Z[ω] 1 Abs irr m b g M view
0 Q(ω) 5 a o χ2 Z[ω] 1 Abs irr m b g M view
0 Z[ω] 5 b o χ3 Z[ω] 1 Abs irr m b g M view
0 Z 6 + χ4 Z 1 Abs irr m b g M view
0 Z[ω] 10 ? m b g M view
0 Z[ω] 10 a o χ5 ? m b g M view
0 Z[ω] 10 b o χ6 ? m b g M view
0 Z 15 a ? m b g M view
0 Z 15 b ? m b g M view
0 Z 20 ? m b g M view
0 Z 24 ? m b g M view
0 Z 30 a ? m b g M view
0 Z[ω] 30 b ? m b g M view
0 Z[ω] 30 c o χ13 ? m b g M view
0 Z[ω] 40 a o χ14 ? m b g M view
0 Z[ω] 40 b o χ15 ? m b g M view
0 Z[ω] 45 a ? m b g M view
0 Z[ω] 45 b o χ17 ? m b g M view
0 Z 60 ? m b g M view
0 Z 64 + χ19 ? m b g M view
0 Z 80 χ14 + χ15 ? m b g M view
0 Z 81 + χ20 ? m b g M view
Char Ring Dim ID Ind Character Char Rng H1 H2 Schur Irr Files
2 GF(4) 4 a Abs irr m b g M view
Char Ring Dim ID Ind Character Char Rng H1 H2 Schur Irr Files
3 GF(3) 5 Abs irr m b g M view
3 GF(3) 10 Abs irr m b g M view
3 GF(3) 14 Abs irr m b g M view
3 GF(3) 25 Abs irr m b g M view
3 GF(3) 81 Abs irr m b g M view
Char Ring Dim ID Ind Character Char Rng H1 H2 Schur Irr Files
5 GF(25) 5 a Abs irr m b g M view
5 GF(5) 6 Abs irr m b g M view
5 GF(25) 10 b Abs irr m b g M view