How to input the stabilizer type of 𝔇12-orbits

There are 31 different conjugacy classes of subgroups of 𝔇12 which occur as stabilizers of tone rows. Prescribe the stabilizer type by choosing a number from 1 to 31.
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

Database on tone rows and tropes
harald.fripertinger "at" uni-graz.at
January 2, 2019