Permutation Representations
| Points | ID | Prim | Trans | Rank | Suborbits | Char | Stab | Files | |
|---|---|---|---|---|---|---|---|---|---|
| 11 | Primitive | 4 | 2 | 1, 10 | 1 + 10a | M10 = A6.23 | m b g M | view | |
| 12 | Primitive | 3 | 2 | 1, 11 | 1 + 11 | L2(11) | m b g M | view | |
| 55 | Primitive | 1 | 3 | 1, 18, 36 | 1 + 10a + 44 | 32:SD16 = 32:8:3 2 | m b g M | view | |
| 66 | Primitive | 1 | 4 | 1, 15, 20, 30 | 1 + 10a + 11 + 44 | S5 | m b g M | view | |
| 165 | Primitive | 1 | 8 | 1, 8, 12, 244, 48 | 1 + 10a + 11 + 442 + 55 | 2.S4+ | m b g M | view |
Matrix Representations
| Char | Ring | Dim | ID | Ind | Character | Char Rng | H1 | H2 | Schur | Irr | Files | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | Z | 10 | a | + | χ2 | Z | 1 | Abs irr | m b g M | view | ||
| 0 | Z[i2] | 10 | b | o | χ3 | Z[i2] | 1 | Abs irr | m b g M | view | ||
| 0 | Z[i2] | 10 | c | o | χ4 | Z[i2] | 1 | Abs irr | m b g M | view | ||
| 0 | Z | 11 | + | χ5 | Z | 1 | Abs irr | m b g M | view | |||
| 0 | Z | 20 | χ3 + χ4 | Z | Irr not abs irr | m b g M | view | |||||
| 0 | Z | 32 | χ6 + χ7 | Z | Irr not abs irr | m b g M | view | |||||
| 0 | Z | 44 | + | χ8 | Z | 1 | Abs irr | m b g M | view | |||
| 0 | Z | 45 | + | χ9 | Z | 1 | Abs irr | m b g M | view | |||
| 0 | Z | 55 | + | χ10 | Z | 1 | Abs irr | m b g M | view | |||
| Char | Ring | Dim | ID | Ind | Character | Char Rng | H1 | H2 | Schur | Irr | Files | |
| 2 | GF(2) | 10 | + | 1 | 1 | Abs irr | m b g M | view | ||||
| 2 | GF(4) | 16 | a | o | 0 | 0 | Abs irr | m b g M | view | |||
| 2 | GF(4) | 16 | b | o | 0 | 0 | Abs irr | m b g M | view | |||
| 2 | GF(2) | 32 | 0 | 0 | Irr not abs irr | m b g M | view | |||||
| 2 | GF(2) | 44 | + | 1 | 1 | Abs irr | m b g M | view | ||||
| Char | Ring | Dim | ID | Ind | Character | Char Rng | H1 | H2 | Schur | Irr | Files | |
| 3 | GF(3) | 5 | a | o | 0 | 0 | Abs irr | m b g M | view | |||
| 3 | GF(3) | 5 | b | o | 1 | 0 | Abs irr | m b g M | view | |||
| 3 | GF(3) | 10 | a | + | 0 | 1 | Abs irr | m b g M | view | |||
| 3 | GF(3) | 10 | b | o | 0 | 0 | Abs irr | m b g M | view | |||
| 3 | GF(3) | 10 | c | o | 1 | 1 | Abs irr | m b g M | view | |||
| 3 | GF(3) | 24 | + | 0 | 1 | Abs irr | m b g M | view | ||||
| 3 | GF(3) | 45 | + | 0 | 0 | Abs irr | m b g M | view | ||||
| Char | Ring | Dim | ID | Ind | Character | Char Rng | H1 | H2 | Schur | Irr | Files | |
| 5 | GF(5) | 10 | a | + | 0 | 0 | Abs irr | m b g M | view | |||
| 5 | GF(25) | 10 | b | o | 0 | 0 | Abs irr | m b g M | view | |||
| 5 | GF(25) | 10 | c | o | 0 | 0 | Abs irr | m b g M | view | |||
| 5 | GF(5) | 11 | + | 0 | 0 | Abs irr | m b g M | view | ||||
| 5 | GF(5) | 16 | a | o | 1 | 1 | Abs irr | m b g M | view | |||
| 5 | GF(5) | 16 | b | o | 0 | 0 | Abs irr | m b g M | view | |||
| 5 | GF(5) | 20 | 0 | 0 | Irr not abs irr | m b g M | view | |||||
| 5 | GF(5) | 45 | + | 0 | 0 | Abs irr | m b g M | view | ||||
| 5 | GF(5) | 55 | + | 0 | 0 | Abs irr | m b g M | view | ||||
| Char | Ring | Dim | ID | Ind | Character | Char Rng | H1 | H2 | Schur | Irr | Files | |
| 11 | GF(11) | 9 | + | 1 | 0 | Abs irr | m b g M | view | ||||
| 11 | GF(11) | 10 | a | o | 0 | 0 | Abs irr | m b g M | view | |||
| 11 | GF(11) | 10 | b | o | 0 | 1 | Abs irr | m b g M | view | |||
| 11 | GF(11) | 11 | + | 0 | 0 | Abs irr | m b g M | view | ||||
| 11 | GF(11) | 16 | + | 0 | 0 | Abs irr | m b g M | view | ||||
| 11 | GF(11) | 44 | + | 0 | 0 | Abs irr | m b g M | view | ||||
| 11 | GF(11) | 55 | + | 0 | 0 | Abs irr | m b g M | view |