How to input the stabilizer type of Aff1(Z12) × Aff1(Z12)-orbits

There are 90 different conjugacy classes of subgroups of Aff1(Z12) × Aff1(Z12) which occur as stabilizers of tone rows. Prescribe the stabilizer type by choosing a number from 1 to 90.
name generators size of the group size of the class number of orbits
X1 identity 1 1 205035
X2 (TI,R) 2 36
X3 (I,SR) 2 36
X4 (IQ,SRF) 2 4
X5 (T3IQ,S4RF) 2 4
X6 (T2Q,S2F) 2 9
X7 (Q,F) 2 9
X8 (TI,S6) 2 6
X9 (T6,R) 2 6
X10 (T2Q,R) 2 18
X11 (T3IQ,R) 2 12
X12 (TI,S2F) 2 18
X13 (T2Q,S6) 2 3
X14 (T3IQ,S6) 2 2
X15 (TI,S4RF) 2 12
X16 (T6,S4RF) 2 2
X17 (T6,S2F) 2 3
X18 (T3IQ,S2F) 2 6
X19 (T2Q,S4RF) 2 6
X20 (T6,S6) 2 1
X21 (T4,S4) 3 2
X22 (I,SR), (T6Q,S6F) 4 36
X23 (TI,R), (T4Q,S8F) 4 36
X24 (I,SR), (Q,F) 4 36
X25 (TI,R), (T10Q,S2F) 4 36
X26 (TI,S6), (T6,R) 4 36
X27 (TI,R), (T6,S6) 4 18
X28 (TI,R), (T3IQ,S6) 4 36
X29 (TI,R), (T10Q,S6) 4 36
X30 (TQ,SF) 4 18
X31 (T3IQ,R), (T2Q,S2F) 4 36
X32 (TI,R), (T7I,S2F) 4 36
X33 (TI,R), (T6,S2F) 4 36
X34 (TI,R), (T3IQ,S2F) 4 36
X35 (T2Q,R), (T3IQ,S2F) 4 36
X36 (T3IQ,R), (T6,S10RF) 4 12
X37 (T6,R), (TI,S2F) 4 36
X38 (T6,R), (T3IQ,S2F) 4 12
X39 (TI,S6), (T3IQ,R) 4 36
X40 (T6,S6), (IQ,SRF) 4 2
X41 (T3I,S4RF), (Q,F) 4 36
X42 (TI,S6), (T6,S4RF) 4 12
X43 (T6,R), (T3IQ,S6) 4 12
X44 (TI,S2F), (T3IQ,S6R) 4 36
X45 (T6Q,S4R), (Q,F) 4 18
X46 (TI,S2F), (T4Q,S8F) 4 18
X47 (T3IQ,S6), (TI,S4RF) 4 12
X48 (TI,S6), (T3IQ,S10RF) 4 12
X49 (T6,S4RF), (T3IQ,S6) 4 4
X50 (T3I,S6), (Q,F) 4 18
X51 (T6,S2F), (T6Q,S6) 4 9
X52 (T6,S2F), (T3IQ,R) 4 12
X53 (TI,S2F), (T10Q,R) 4 36
X54 (TI,S4RF), (T10Q,S6) 4 12
X55 (T6,S4R), (Q,F) 4 18
X56 (T6,S6), (TI,S4RF) 4 6
X57 (TQ,S3) 4 6
X58 (T6,S6), (T3IQ,R) 4 6
X59 (T3,SF) 4 6
X60 (TI,R), (T4,S4) 6 24
X61 (T4,S4), (IQ,SRF) 6 8
X62 (T4,S4), (T2Q,R) 6 12
X63 (TI,S2F), (T4,S4) 6 12
X64 (T6,S6), (I,SR), (Q,F) 8 18
X65 (T3IQ,S6), (T6Q,S4R), (Q,F) 8 36
X66 (T3I,S4R), (T6,S6F), (Q,F) 8 36
X67 (TI,R), (TQ,S5F) 8 36
X68 (T6,R), (TI,S6), (T4Q,S8F) 8 36
X69 (TI,S6), (T4Q,F), (T6,S4RF) 8 36
X70 (TQ,S3), (TI,S4RF) 8 12
X71 (T3,SF), (IQ,SRF) 8 12
X72 (T6,S4R), (T9I,S6F), (Q,F) 8 36
X73 (T6,S6), (T3I,S4R), (Q,F) 8 18
X74 (T3,S3), (Q,F) 8 18
X75 (T3,S3), (I,SR) 8 36
X76 (T3Q,S3F), (I,SR) 8 36
X77 (T3,SF), (I,S5R) 8 36
X78 (T3Q,S3), (I,SR) 8 36
X79 (T6,S6), (T3I,S4RF), (Q,F) 8 18
X80 (T3,S3F), (Q,F) 8 18
X81 (I,SR), (T2IQ,S3RF) 12 24
X82 (T2,RF), (TI,S2F) 12 24
X83 (T7IQ,S2RF), (T2Q,S4R) 12 24
X84 (T7IQ,S2RF), (TI,R) 12 24
X85 (T7IQ,S10), (TI,R) 12 24
X86 (T3,SF), (I,S5R), (Q,S4F) 16 36
X87 (T3,S3), (I,SR), (Q,F) 16 36
X88 (T2,S2), (TI,R), (TQ,S5F) 24 24
X89 (T2,RF), (TI,S2F), (Q,S4F) 24 24
X90 (T,S), (I,SR), (Q,F) 48 24

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