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Dimension Conductor Group Root number Parity
Smallest permutation Ramified Unramified primes Ramified prime count Frobenius-Schur
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Galois conjugate representations are grouped into single lines.
Label Dimension Conductor Artin stem field GG Ind χ(c)\chi(c)
3.229.4t5.a.a 33 229 229 4.0.229.1 S4S_4 11 −1-1
3.257.4t5.a.a 33 257 257 4.0.257.1 S4S_4 11 −1-1
3.283.4t5.b.a 33 283 283 4.2.283.1 S4S_4 11 11
3.331.4t5.a.a 33 331 331 4.2.331.1 S4S_4 11 11
3.332.6t11.a.a 33 22⋅83 2^{2} \cdot 83 6.0.27556.1 S4×C2S_4\times C_2 11 −1-1
3.341.6t11.c.a 33 11⋅31 11 \cdot 31 6.0.10571.1 S4×C2S_4\times C_2 11 −1-1
3.437.6t11.b.a 33 19⋅23 19 \cdot 23 6.0.10051.1 S4×C2S_4\times C_2 11 −1-1
3.472.6t11.a.a 33 23⋅59 2^{3} \cdot 59 6.0.27848.1 S4×C2S_4\times C_2 11 −1-1
3.491.4t5.b.a 33 491 491 4.2.491.1 S4S_4 11 11
3.563.4t5.b.a 33 563 563 4.2.563.1 S4S_4 11 11
3.592.4t5.a.a 33 24⋅37 2^{4} \cdot 37 4.0.592.1 S4S_4 11 −1-1
3.597.6t11.b.a 33 3⋅199 3 \cdot 199 6.0.118803.1 S4×C2S_4\times C_2 11 −1-1
3.637.6t6.a.a 33 72⋅13 7^{2} \cdot 13 6.2.31213.1 A4×C2A_4\times C_2 11 −1-1
3.643.4t5.a.a 33 643 643 4.2.643.1 S4S_4 11 11
3.688.4t5.b.a 33 24⋅43 2^{4} \cdot 43 4.2.688.1 S4S_4 11 11
3.697.4t5.a.a 33 17⋅41 17 \cdot 41 4.0.697.1 S4S_4 11 −1-1
3.717.6t11.b.a 33 3⋅239 3 \cdot 239 6.0.171363.1 S4×C2S_4\times C_2 11 −1-1
3.731.4t5.a.a 33 17⋅43 17 \cdot 43 4.2.731.1 S4S_4 11 11
3.740.6t11.c.a 33 22⋅5⋅37 2^{2} \cdot 5 \cdot 37 6.2.109520.1 S4×C2S_4\times C_2 11 −1-1
3.749.6t11.b.a 33 7⋅107 7 \cdot 107 6.0.80143.1 S4×C2S_4\times C_2 11 −1-1
3.751.4t5.a.a 33 751 751 4.2.751.1 S4S_4 11 11
3.761.4t5.a.a 33 761 761 4.0.761.1 S4S_4 11 −1-1
3.788.4t5.a.a 33 22⋅197 2^{2} \cdot 197 4.0.788.1 S4S_4 11 −1-1
3.804.6t11.a.a 33 22⋅3⋅67 2^{2} \cdot 3 \cdot 67 6.0.215472.1 S4×C2S_4\times C_2 11 −1-1
3.805.6t11.a.a 33 5⋅7⋅23 5 \cdot 7 \cdot 23 6.0.18515.1 S4×C2S_4\times C_2 11 −1-1
3.844.6t11.a.a 33 22⋅211 2^{2} \cdot 211 6.0.178084.1 S4×C2S_4\times C_2 11 −1-1
3.845.6t6.a.a 33 5⋅132 5 \cdot 13^{2} 6.2.142805.1 A4×C2A_4\times C_2 11 −1-1
3.848.4t5.b.a 33 24⋅53 2^{4} \cdot 53 4.2.848.1 S4S_4 11 11
3.856.6t11.a.a 33 23⋅107 2^{3} \cdot 107 6.2.91592.1 S4×C2S_4\times C_2 11 11
3.892.4t5.a.a 33 22⋅223 2^{2} \cdot 223 4.0.892.1 S4S_4 11 −1-1
3.912.6t11.b.a 33 24⋅3⋅19 2^{4} \cdot 3 \cdot 19 6.0.69312.1 S4×C2S_4\times C_2 11 −1-1
3.921.6t11.a.a 33 3⋅307 3 \cdot 307 6.0.282747.1 S4×C2S_4\times C_2 11 −1-1
3.944.6t11.a.a 33 24⋅59 2^{4} \cdot 59 6.0.55696.1 S4×C2S_4\times C_2 11 −1-1
3.963.6t11.a.a 33 32⋅107 3^{2} \cdot 107 6.4.309123.1 S4×C2S_4\times C_2 11 11
3.976.4t5.b.a 33 24⋅61 2^{4} \cdot 61 4.2.976.1 S4S_4 11 11
3.981.6t11.b.a 33 32⋅109 3^{2} \cdot 109 6.0.320787.1 S4×C2S_4\times C_2 11 −1-1
3.985.4t5.a.a 33 5⋅197 5 \cdot 197 4.0.985.1 S4S_4 11 −1-1
3.988.6t11.a.a 33 22⋅13⋅19 2^{2} \cdot 13 \cdot 19 6.2.75088.1 S4×C2S_4\times C_2 11 11
3.989.6t11.b.a 33 23⋅43 23 \cdot 43 6.0.22747.1 S4×C2S_4\times C_2 11 −1-1
3.1003.6t11.b.a 33 17⋅59 17 \cdot 59 6.2.59177.1 S4×C2S_4\times C_2 11 11
3.1016.4t5.a.a 33 23⋅127 2^{3} \cdot 127 4.0.1016.1 S4S_4 11 −1-1
3.1076.4t5.a.a 33 22⋅269 2^{2} \cdot 269 4.0.1076.1 S4S_4 11 −1-1
3.1099.4t5.a.a 33 7⋅157 7 \cdot 157 4.2.1099.1 S4S_4 11 11
3.1101.6t11.b.a 33 3⋅367 3 \cdot 367 6.0.404067.1 S4×C2S_4\times C_2 11 −1-1
3.1107.4t5.a.a 33 33⋅41 3^{3} \cdot 41 4.2.1107.1 S4S_4 11 11
3.1112.6t11.b.a 33 23⋅139 2^{3} \cdot 139 6.0.154568.1 S4×C2S_4\times C_2 11 −1-1
3.1129.4t5.a.a 33 1129 1129 4.0.1129.1 S4S_4 11 −1-1
3.1137.6t11.b.a 33 3⋅379 3 \cdot 379 6.0.430923.1 S4×C2S_4\times C_2 11 −1-1
3.1147.6t11.b.a 33 31⋅37 31 \cdot 37 6.2.35557.1 S4×C2S_4\times C_2 11 11
3.1192.4t5.a.a 33 23⋅149 2^{3} \cdot 149 4.2.1192.1 S4S_4 11 11
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