| name | generators | size of the group | size of the class | number of orbits |
| Z1 | identity | 1 | 1 | 410978 |
| Z2 | P | 2 | 24 | |
| Z3 | (TI,R) | 2 | 36 | |
| Z4 | (I,SR) | 2 | 36 | |
| Z5 | (T6,R) | 2 | 12 | |
| Z6 | (T6,S6) | 2 | 1 | |
| Z7 | (T4,S4) | 3 | 2 | |
| Z8 | (TI,R), (I,SR) o P | 4 | 72 | |
| Z9 | (I,SR), P | 4 | 72 | |
| Z10 | (T6,S6), P | 4 | 12 | |
| Z11 | (T6,R), (TI,S6) | 4 | 36 | |
| Z12 | (TI,R), (T6,S6) | 4 | 18 | |
| Z13 | (TI,R), (T,SR) o P | 4 | 72 | |
| Z14 | (I,SR), (T6,S6) | 4 | 18 | |
| Z15 | (T6,S0) o P | 4 | 12 | |
| Z16 | (T4,S4), (I,SR) o P | 6 | 8 | |
| Z17 | (TI,R), (T4,S4) | 6 | 24 | |
| Z18 | (TI,S6), P | 8 | 72 | |
| Z19 | (I,SR), (T6,S6), P | 8 | 18 | |
| Z20 | (TI,R), (T6,S6), (I,SR) o P | 8 | 18 | |
| Z21 | (TI,R), (T4,S2) o P | 8 | 36 | |
| Z22 | (T3,S3), (I,SR) o P | 8 | 6 | |
| Z23 | (I,SR), (T3,S3) o P | 8 | 36 | |
| Z24 | (I,SR), (T3,S3) | 8 | 36 | |
| Z25 | (TI,R), (T9,S7) o P | 12 | 48 | |
| Z26 | (I,SR), (T4,S4), P | 12 | 48 | |
| Z27 | (I,SR), (T3,S3), P | 16 | 36 | |
| Z28 | (TI,R), (T2,S2), (I,SR) o P | 24 | 12 | |
| Z29 | (TI,R), (T2,S2), (T2,S0) o P | 24 | 12 | |
| Z30 | (I,SR), (T,S), P | 48 | 12 | |
| Z31 | (I,SR), (T,S5), P | 48 | 12 |