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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$4T1
C2XC2$V_4$4T2
V4$V_4$4T2
D2$V_4$4T2
D4$D_4$4T3, 8T4
A4$A_4$4T4, 6T4, 12T4
S4$S_4$4T5, 6T7, 6T8, 8T14, 12T8, 12T9
C5$C_5$5T1
D5$D_5$5T2, 10T2
F5$F_5$5T3, 10T4
A5$A_5$5T4, 6T12, 10T7, 12T33
PSL(2,5)$A_5$5T4, 6T12, 10T7, 12T33
PGL(2,5)$S_5$5T5, 6T14, 10T12, 10T13, 12T74
S5$S_5$5T5, 6T14, 10T12, 10T13, 12T74
C6$C_6$6T1
D6$S_3\times C_2$6T3, 12T3
C3XS3$S_3\times C_3$6T5, 9T4
S3XC3$S_3\times C_3$6T5, 9T4
S3XS3$S_3^2$6T9, 9T8, 12T16
PSL(2,9)$A_6$6T15, 10T26
A6$A_6$6T15, 10T26
S6$S_6$6T16, 10T32, 12T183, 12T183
C7$C_7$7T1
D7$D_7$7T2, 14T2
F7$F_7$7T4, 14T4, 21T4
PSL(2,7)$\GL(3,2)$7T5, 8T37
GL(3,2)$\GL(3,2)$7T5, 8T37
A7$A_7$7T6
S7$S_7$7T7
C8$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$8T6, 16T7
SL(2,3)$\SL(2,3)$8T12
GL(2,3)$\textrm{GL(2,3)}$8T23
PGL(2,7)$\PGL(2,7)$8T43
A8$A_8$8T49
S8$S_8$8T50
C9$C_9$9T1
C3XC3$C_3^2$9T2
D9$D_9$9T3
M9$C_3^2:Q_8$9T14, 12T47
PSL(2,8)$\PSL(2,8)$9T27
A9$A_9$9T33
S9$S_9$9T34
C10$C_{10}$10T1
D10$D_{10}$10T3
PGL(2,9)$\PGL(2,9)$10T30, 12T182
M10$M_{10}$10T31, 12T181
A10$A_{10}$10T44
S10$S_{10}$10T45
C11$C_{11}$11T1
D11$D_{11}$11T2, 22T2
F11$F_{11}$11T4, 22T4
PSL(2,11)$\PSL(2,11)$11T5, 12T272
M11$M_{11}$11T6
A11$A_{11}$11T7
S11$S_{11}$11T8
C12$C_{12}$12T1
C2XC6$C_6\times C_2$12T2
C6XC2$C_6\times C_2$12T2
A12$A_{12}$12T300
S12$S_{12}$12T301
C13$C_{13}$13T1
D13$D_{13}$13T2
F13$F_{13}$13T6
A13$A_{13}$13T8
S13$S_{13}$13T9
C14$C_{14}$14T1
D14$D_{14}$14T3
PGL(2,13)$\PGL(2,13)$14T39
A1414T6214T62
S1414T6314T63
C15$C_{15}$15T1
A1515T10315T103
S1515T10415T104
C16$C_{16}$16T1
Q16$Q_{16}$16T14
A16$A_{16}$16T1953
S16$S_{16}$16T1954
C17$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}$18T1
PGL(2,17)$\PGL(2,17)$18T468
A18$A_{18}$18T982
S18$S_{18}$18T983
C19$C_{19}$19T1
A19$A_{19}$19T7
S19$S_{19}$19T8
C20$C_{20}$20T1
PGL(2,19)$\PGL(2,19)$20T362
A2020T111620T1116
S2020T111720T1117
C21$C_{21}$21T1
A2121T16321T163
S2121T16421T164
C22$C_{22}$22T1
D2222T322T3
A2222T5822T58
S2222T5922T59
C23$C_{23}$23T1
D23$D_{23}$23T2
F23$C_{23}:C_{11}$23T3
M23$M_{23}$23T5
A23$A_{23}$23T6
S23$S_{23}$23T7