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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\(t\)
V4$C_2^2$4T2
C2XC2$C_2^2$4T2
F5$F_5$5T3, 10T4, 20T5
PSL(2,5)$A_5$5T4, 6T12, 10T7, 12T33, 15T5, 20T15, 30T9
PGL(2,5)$S_5$5T5, 6T14, 10T12, 10T13, 12T74, 15T10, 20T30, 20T32, 20T35, 24T202, 30T22, 30T25, 30T27, 40T62
S3XC3$S_3\times C_3$6T5, 9T4, 18T3
S3XS3$S_3^2$6T9, 9T8, 12T16, 18T9, 18T11, 36T13
PSL(2,9)$A_6$6T15, 10T26, 15T20, 20T89, 30T88, 36T555, 40T304, 45T49
F7$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)$7T5, 8T37, 14T10, 21T14, 24T284, 28T32, 42T37, 42T38
C4XC2$C_4\times C_2$8T2
C2XC2XC2$C_2^3$8T3
Q8$Q_8$8T5
SL(2,3)$\SL(2,3)$8T12, 24T7
GL(2,3)$\textrm{GL(2,3)}$8T23, 16T66, 24T22
PGL(2,7)$\PGL(2,7)$8T43, 14T16, 16T713, 21T20, 24T707, 28T42, 28T46, 42T81, 42T82, 42T83
C3XC3$C_3^2$9T2
M9$C_3^2:Q_8$9T14, 12T47, 18T35, 24T82, 36T55
PSL(2,8)$\PSL(2,8)$9T27, 28T70, 36T712
PGL(2,9)$\PGL(2,9)$10T30, 12T182, 20T146, 30T171, 36T1254, 40T590, 45T110
M10$M_{10}$10T31, 12T181, 20T148, 20T150, 30T162, 36T1253, 40T591, 45T109
F11$F_{11}$11T4, 22T4
PSL(2,11)$\PSL(2,11)$11T5, 12T179
M11$M_{11}$11T6, 12T272, 22T22
C6XC2$C_6\times C_2$12T2
C3:C4$C_3 : C_4$12T5
M12$M_{12}$12T295
F13$F_{13}$13T6, 26T8, 39T11
PSL(3,3)$\PSL(3,3)$13T7, 26T39, 39T43
PSL(2,13)$\PSL(2,13)$14T30, 28T120, 42T176
PGL(2,13)$\PGL(2,13)$14T39, 28T201, 42T284
Q8XC2$Q_8\times C_2$16T7
C4:C4$C_4:C_4$16T8
Q16$Q_{16}$16T14
F17$F_{17}$17T5
PSL(2,17)$\PSL(2,16)$17T6
PGL(2,17)$\PGL(2,17)$18T468
C5:C4$C_5:C_4$20T2
PGL(2,19)t20n36220T362, 40T5409
M22$M_{22}$22T38
F23$C_{23}:C_{11}$23T3
M23$M_{23}$23T5
Q8XC3$C_3\times Q_8$24T4
C3:Q8$C_3:Q_8$24T5
C3:C8$C_3:C_8$24T8
M24$M_{24}$24T24680
PSP(4,3)$\PSp(4,3)$27T993, 36T12781, 40T14344, 40T14345, 45T666
C7:C4$C_7:C_4$28T3
PSU(3,3)$\PSU(3,3)$28T323, 36T6815
Q32$Q_{32}$32T51
C5:C8$C_5:C_8$40T3