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Label Degree Type Faithful Field of Traces $\Q$-character Group Image Image Order Kernel Kernel Order Center
648.572.1a $1$ R \(\Q\) 648.572.1a $C_3^3:S_4$ $C_1$ $1$ 1.a1 $648$ 1.a1
648.572.1b $1$ R \(\Q\) 648.572.1b $C_3^3:S_4$ $C_2$ $2$ 2.a1 $324$ 1.a1
648.572.1c1 $1$ C \(\Q(\sqrt{-3}) \) 648.572.1c $C_3^3:S_4$ $C_3$ $3$ 3.a1 $216$ 1.a1
648.572.1c2 $1$ C \(\Q(\sqrt{-3}) \) 648.572.1c $C_3^3:S_4$ $C_3$ $3$ 3.a1 $216$ 1.a1
648.572.1d1 $1$ C \(\Q(\sqrt{-3}) \) 648.572.1d $C_3^3:S_4$ $C_6$ $6$ 6.c1 $108$ 1.a1
648.572.1d2 $1$ C \(\Q(\sqrt{-3}) \) 648.572.1d $C_3^3:S_4$ $C_6$ $6$ 6.c1 $108$ 1.a1
648.572.2a $2$ R \(\Q\) 648.572.2a $C_3^3:S_4$ $S_3$ $6$ 6.b1 $108$ 6.b1
648.572.2b $2$ R \(\Q\) 648.572.2b $C_3^3:S_4$ $S_3$ $6$ 6.b1 $108$ 6.b1
648.572.2c $2$ R \(\Q\) 648.572.2c $C_3^3:S_4$ $S_3$ $6$ 6.b1 $108$ 6.b1
648.572.2d $2$ R \(\Q\) 648.572.2d $C_3^3:S_4$ $S_3$ $6$ 6.a1 $108$ 6.a1
648.572.2e1 $2$ C \(\Q(\sqrt{-3}) \) 648.572.2e $C_3^3:S_4$ $C_3\times S_3$ $18$ 18.b1 $36$ 6.a1
648.572.2e2 $2$ C \(\Q(\sqrt{-3}) \) 648.572.2e $C_3^3:S_4$ $C_3\times S_3$ $18$ 18.b1 $36$ 6.a1
648.572.2f1 $2$ C \(\Q(\sqrt{-3}) \) 648.572.2f $C_3^3:S_4$ $C_3\times S_3$ $18$ 18.c1 $36$ 6.b1
648.572.2f2 $2$ C \(\Q(\sqrt{-3}) \) 648.572.2f $C_3^3:S_4$ $C_3\times S_3$ $18$ 18.c1 $36$ 6.b1
648.572.2g1 $2$ C \(\Q(\sqrt{-3}) \) 648.572.2g $C_3^3:S_4$ $C_3\times S_3$ $18$ 18.c1 $36$ 6.b1
648.572.2g2 $2$ C \(\Q(\sqrt{-3}) \) 648.572.2g $C_3^3:S_4$ $C_3\times S_3$ $18$ 18.c1 $36$ 6.b1
648.572.2h1 $2$ C \(\Q(\sqrt{-3}) \) 648.572.2h $C_3^3:S_4$ $C_3\times S_3$ $18$ 18.c1 $36$ 6.b1
648.572.2h2 $2$ C \(\Q(\sqrt{-3}) \) 648.572.2h $C_3^3:S_4$ $C_3\times S_3$ $18$ 18.c1 $36$ 6.b1
648.572.3a $3$ R \(\Q\) 648.572.3a $C_3^3:S_4$ $S_4$ $24$ 24.a1 $27$ 24.a1
648.572.3b $3$ R \(\Q\) 648.572.3b $C_3^3:S_4$ $S_4$ $24$ 24.a1 $27$ 24.a1
648.572.3c1 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3c $C_3^3:S_4$ $C_3^2:S_3$ $54$ 54.a1 $12$ 18.a1
648.572.3c2 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3c $C_3^3:S_4$ $C_3^2:S_3$ $54$ 54.a1 $12$ 18.a1
648.572.3d1 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3d $C_3^3:S_4$ $C_3^2:S_3$ $54$ 54.a1 $12$ 18.a1
648.572.3d2 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3d $C_3^3:S_4$ $C_3^2:S_3$ $54$ 54.a1 $12$ 18.a1
648.572.3e1 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3e $C_3^3:S_4$ $C_3^2:S_3$ $54$ 54.a1 $12$ 18.a1
648.572.3e2 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3e $C_3^3:S_4$ $C_3^2:S_3$ $54$ 54.a1 $12$ 18.a1
648.572.3f1 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3f $C_3^3:S_4$ $C_3\times S_4$ $72$ 72.b1 $9$ 24.a1
648.572.3f2 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3f $C_3^3:S_4$ $C_3\times S_4$ $72$ 72.b1 $9$ 24.a1
648.572.3g1 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3g $C_3^3:S_4$ $C_3^2:S_3$ $54$ 54.a1 $12$ 18.a1
648.572.3g2 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3g $C_3^3:S_4$ $C_3^2:S_3$ $54$ 54.a1 $12$ 18.a1
648.572.3h1 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3h $C_3^3:S_4$ $C_3^2:S_3$ $54$ 54.a1 $12$ 18.a1
648.572.3h2 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3h $C_3^3:S_4$ $C_3^2:S_3$ $54$ 54.a1 $12$ 18.a1
648.572.3i1 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3i $C_3^3:S_4$ $C_3^2:S_3$ $54$ 54.a1 $12$ 18.a1
648.572.3i2 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3i $C_3^3:S_4$ $C_3^2:S_3$ $54$ 54.a1 $12$ 18.a1
648.572.3j1 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3j $C_3^3:S_4$ $C_3\times S_4$ $72$ 72.b1 $9$ 24.a1
648.572.3j2 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3j $C_3^3:S_4$ $C_3\times S_4$ $72$ 72.b1 $9$ 24.a1
648.572.3k1 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3k $C_3^3:S_4$ $C_3^2:S_4$ $216$ 216.a1 $3$ 72.a1
648.572.3k2 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3k $C_3^3:S_4$ $C_3^2:S_4$ $216$ 216.a1 $3$ 72.a1
648.572.3l1 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3l $C_3^3:S_4$ $C_3^2:S_4$ $216$ 216.a1 $3$ 72.a1
648.572.3l2 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3l $C_3^3:S_4$ $C_3^2:S_4$ $216$ 216.a1 $3$ 72.a1
648.572.3m1 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3m $C_3^3:S_4$ $C_3^2:S_4$ $216$ 216.a1 $3$ 72.a1
648.572.3m2 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3m $C_3^3:S_4$ $C_3^2:S_4$ $216$ 216.a1 $3$ 72.a1
648.572.3n1 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3n $C_3^3:S_4$ $C_3^2:S_4$ $216$ 216.a1 $3$ 72.a1
648.572.3n2 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3n $C_3^3:S_4$ $C_3^2:S_4$ $216$ 216.a1 $3$ 72.a1
648.572.3o1 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3o $C_3^3:S_4$ $C_3^2:S_4$ $216$ 216.a1 $3$ 72.a1
648.572.3o2 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3o $C_3^3:S_4$ $C_3^2:S_4$ $216$ 216.a1 $3$ 72.a1
648.572.3p1 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3p $C_3^3:S_4$ $C_3^2:S_4$ $216$ 216.a1 $3$ 72.a1
648.572.3p2 $3$ C \(\Q(\sqrt{-3}) \) 648.572.3p $C_3^3:S_4$ $C_3^2:S_4$ $216$ 216.a1 $3$ 72.a1
648.572.6a $6$ R \(\Q\) 648.572.6a $C_3^3:S_4$ $C_3:S_4$ $72$ 72.a1 $9$ 72.a1
648.572.6b1 $6$ C \(\Q(\sqrt{-3}) \) 648.572.6b $C_3^3:S_4$ $C_3^2:S_4$ $216$ 216.b1 $3$ 72.a1
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