Permutation Representations
| Points | ID | Prim | Trans | Rank | Suborbits | Char | Stab | Files | |
|---|---|---|---|---|---|---|---|---|---|
| 5 | Primitive | 5 | 2 | 1, 4 | 1+ + 4+ | S4 | m b g M | view | |
| 6 | Primitive | 3 | 2 | 1, 5 | 1+ + 5− | 5:4 = F20 | m b g M | view | |
| 10 | Primitive | 1 | 3 | 1, 3, 6 | 1+ + 4+ + 5+ | D12 = S3 × 2 | m b g M | view |
Matrix Representations
| Char | Ring | Dim | ID | Ind | Character | Char Rng | H1 | H2 | Schur | Irr | Files | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | GF(2) | 4 | a | − | φ2+3 | Z | 1 | 0 | 1 | Abs irr | m b g M | view |
| 2 | GF(2) | 4 | b | + | φ4 | Z | 0 | 0 | 1 | Abs irr | m b g M | view |
| 3 | GF(3) | 4 | + | φ4, 0 | Z | 0 | 0 | 1 | Abs irr | m b g M | view | |
| 3 | GF(3) | 6 | + | φ2+3 | Z | 0 | 0 | 1 | Abs irr | m b g M | view | |
| 5 | GF(5) | 3 | + | φ2, 0 | Z | 1 | 0 | 1 | Abs irr | m b g M | view | |
| 5 | GF(5) | 5 | + | φ3, 0 | Z | 0 | 0 | 1 | Abs irr | m b g M | view |