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Each Galois group is identified by a code "nTt" where \(n\) is its degree and \(t\) and its T-number. One may specify a group by this symbol.

For familiar groups one can use short names from the table below. An abstract group may have more than one representation as a Galois group. Correspondingly, the familiar symbol for a group may represent several Galois groups. These combinations for degree $\leq 11$ are shown below.

AliasGroup\(n\)T\(t\)
S1Trivial1T1
C1Trivial1T1
A1Trivial1T1
A2Trivial1T1
S2$C_2$2T1
C2$C_2$2T1
D1$C_2$2T1
C3$C_3$3T1
A3$C_3$3T1
S3$S_3$3T2, 6T2
D3$S_3$3T2, 6T2
C4$C_4$4T1
C2XC2$C_2^2$4T2
V4$C_2^2$4T2
D2$C_2^2$4T2
D4$D_{4}$4T3, 8T4
A4$A_4$4T4, 6T4, 12T4
S4$S_4$4T5, 6T7, 6T8, 8T14, 12T8, 12T9, 24T10
C5$C_5$5T1
D5$D_{5}$5T2, 10T2
F5$F_5$5T3, 10T4, 20T5
A5$A_5$5T4, 6T12, 10T7, 12T33, 15T5, 20T15, 30T9
PSL(2,5)$A_5$5T4, 6T12, 10T7, 12T33, 15T5, 20T15, 30T9
PGL(2,5)$S_5$5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62
S5$S_5$5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62
C6$C_6$6T1
D6$D_{6}$6T3, 12T3
C3XS3$S_3\times C_3$6T5, 9T4, 18T3
S3XC3$S_3\times C_3$6T5, 9T4, 18T3
S3XS3$S_3^2$6T9, 9T8, 12T16, 18T9, 18T11, 36T13
PSL(2,9)$A_6$6T15, 10T26, 15T20, 20T89, 30T88, 36T555, 40T304, 45T49
A6$A_6$6T15, 10T26, 15T20, 20T89, 30T88, 36T555, 40T304, 45T49
S6$S_6$6T16, 10T32, 12T183, 15T28, 20T145, 20T149, 30T164, 30T166, 30T176, 36T1252, 40T589, 40T592, 45T96
C7$C_7$7T1
D7$D_{7}$7T2, 14T2
F7$F_7$7T4, 14T4, 21T4, 42T4
GL(3,2)$\GL(3,2)$7T5, 8T37, 14T10, 21T14, 24T284, 28T32, 42T37, 42T38
PSL(2,7)$\GL(3,2)$7T5, 8T37, 14T10, 21T14, 24T284, 28T32, 42T37, 42T38
A7$A_7$7T6, 15T47, 21T33, 35T28, 42T294, 42T299
S7$S_7$7T7, 14T46, 21T38, 30T565, 35T31, 42T411, 42T412, 42T413, 42T418
C8$C_8$8T1
C4XC2$C_4\times C_2$8T2
C2XC4$C_4\times C_2$8T2
C2XC2XC2$C_2^3$8T3
Q8$Q_8$8T5
D8$D_{8}$8T6, 16T13
SL(2,3)$\SL(2,3)$8T12, 24T7
GL(2,3)$\textrm{GL(2,3)}$8T23, 16T66, 24T22
PGL(2,7)$\PGL(2,7)$8T43, 14T16, 16T713, 21T20, 24T707, 28T42, 28T46, 42T81, 42T82, 42T83
A8$A_8$8T49, 15T72, 28T433, 35T36
S8$S_8$8T50, 16T1838, 28T502, 30T1153, 35T44
C9$C_9$9T1
C3XC3$C_3^2$9T2
D9$D_{9}$9T3, 18T5
M9$C_3^2:Q_8$9T14, 12T47, 18T35, 24T82, 36T55
PSL(2,8)$\PSL(2,8)$9T27, 28T70, 36T712
A9$A_9$9T33, 36T23796
S9$S_9$9T34, 18T887, 36T28590
C10$C_{10}$10T1
D10$D_{10}$10T3, 20T4
PGL(2,9)$\PGL(2,9)$10T30, 12T182, 20T146, 30T171, 36T1254, 40T590, 45T110
M10$M_{10}$10T31, 12T181, 20T148, 20T150, 30T162, 36T1253, 40T591, 45T109
A10$A_{10}$10T44, 45T1982
S10$S_{10}$10T45, 20T1007, 45T2246
C11$C_{11}$11T1
D11$D_{11}$11T2, 22T2
F11$F_{11}$11T4, 22T4
PSL(2,11)$\PSL(2,11)$11T5, 12T179
M11$M_{11}$11T6, 12T272, 22T22
A11$A_{11}$11T7
S11$S_{11}$11T8, 22T45
C12$C_{12}$12T1
C2XC6$C_6\times C_2$12T2
C6XC2$C_6\times C_2$12T2
D12$D_{12}$12T12, 24T13
A12$A_{12}$12T300
S12$S_{12}$12T301, 24T24748
C13$C_{13}$13T1
D13$D_{13}$13T2, 26T2
F13$F_{13}$13T6, 26T8, 39T11
A13$A_{13}$13T8
S13$S_{13}$13T9, 26T83
C14$C_{14}$14T1
D14$D_{14}$14T3, 28T4
PGL(2,13)$\PGL(2,13)$14T39, 28T201, 42T284
A14A1414T62
S14S1414T63, 28T1755
C15$C_{15}$15T1
D15$D_{15}$15T2, 30T3
A15A1515T103
S15S1515T104, 30T5467
C16$C_{16}$16T1
Q16$Q_{16}$16T14
D16$D_{16}$16T56, 32T31
A16$A_{16}$16T1953
S16$S_{16}$16T1954, 32T2801205
C17$C_{17}$17T1
D17$D_{17}$17T2
F17$F_{17}$17T5
PSL(2,17)$\PSL(2,16)$17T6
A17$A_{17}$17T9
S17$S_{17}$17T10
C18$C_{18}$18T1
D18$D_{18}$18T13
PGL(2,17)$\PGL(2,17)$18T468
A18$A_{18}$18T982
S18$S_{18}$18T983
C19$C_{19}$19T1
D19$D_{19}$19T2
A19$A_{19}$19T7
S19$S_{19}$19T8
C20$C_{20}$20T1
D20$D_{20}$20T10, 40T12
PGL(2,19)t20n36220T362, 40T5409
A20t20n111620T1116
S20t20n111720T1117, 40T315649
C21$C_{21}$21T1
D21$D_{21}$21T5, 42T5
A21A2121T163
S21S2121T164, 42T9215
C22$C_{22}$22T1
D22$D_{22}$22T3, 44T4
A22t22n5822T58
S22t22n5922T59, 44T2028
C23$C_{23}$23T1
D23$D_{23}$23T2, 46T2
F23$C_{23}:C_{11}$23T3
M23$M_{23}$23T5
A23$A_{23}$23T6
S23$S_{23}$23T7, 46T44
C24$C_{24}$24T1
D24$D_{24}$24T34
C25$C_{25}$25T1
D25$D_{25}$25T4
A25$A_{25}$25T210
S25$S_{25}$25T211
C26$C_{26}$26T1
D26$D_{26}$26T3
A26$A_{26}$26T95
S26$S_{26}$26T96
A24$A_{24}$24T24999
S24$S_{24}$24T25000
C27$C_{27}$27T1
D27$D_{27}$27T8
A27$A_{27}$27T2391
S27$S_{27}$27T2392
C28$C_{28}$28T1
D28$D_{28}$28T10
A28$A_{28}$28T1853
S28$S_{28}$28T1854
C29$C_{29}$29T1
D29$D_{29}$29T2
A29$A_{29}$29T7
S29$S_{29}$29T8
C30$C_{30}$30T1
D30$D_{30}$30T14
A30$A_{30}$30T5711
S30$S_{30}$30T5712
C31$C_{31}$31T1
D31$D_{31}$31T2
A31$A_{31}$31T11
S31$S_{31}$31T12
C32$C_{32}$32T33
D32$D_{32}$32T374
C33$C_{33}$33T1
D33$D_{33}$33T3
A33$A_{33}$33T161
S33$S_{33}$33T162
C34$C_{34}$34T1
D34$D_{34}$34T3
A34$A_{34}$34T114
S34$S_{34}$34T115
C35$C_{35}$35T1
D35$D_{35}$35T4
A35$A_{35}$35T406
S35$S_{35}$35T407
C36$C_{36}$36T1
D36$D_{36}$36T47
C37$C_{37}$37T1
D37$D_{37}$37T2
A37$A_{37}$37T10
S37$S_{37}$37T11
C38$C_{38}$38T1
D38$D_{38}$38T3
A38$A_{38}$38T75
S38$S_{38}$38T76
C39$C_{39}$39T1
D39$D_{39}$39T4
A39$A_{39}$39T305
S39$S_{39}$39T306
C40$C_{40}$40T1
D40$D_{40}$40T46
C41$C_{41}$41T1
D41$D_{41}$41T2
A41$A_{41}$41T9
S41$S_{41}$41T10
C42$C_{42}$42T1
D42$D_{42}$42T11
A42$A_{42}$42T9490
S42$S_{42}$42T9491
C43$C_{43}$43T1
D43$D_{43}$43T2
A43$A_{43}$43T9
S43$S_{43}$43T10
C44$C_{44}$44T1
D44$D_{44}$44T9
A44$A_{44}$44T2112
S44$S_{44}$44T2113
C45$C_{45}$45T1
D45$D_{45}$45T4
C46$C_{46}$46T1
D46$D_{46}$46T3
A46$A_{46}$46T55
S46$S_{46}$46T56
A45$A_{45}$45T10922
S45$S_{45}$45T10923
C47$C_{47}$47T1
D47$D_{47}$47T2
A47$A_{47}$47T5
S47$S_{47}$47T6
A36$A_{36}$36T121278
S36$S_{36}$36T121279
A40$A_{40}$40T315841
S40$S_{40}$40T315842
A32$A_{32}$32T2801323
S32$S_{32}$32T2801324