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Label Degree Type Faithful Field of Traces $\Q$-character Group Image Image Order Kernel Kernel Order Center
672.400.1a $1$ R \(\Q\) 672.400.1a $C_{24}:D_{14}$ $C_1$ $1$ 1.a1.a1 $672$ 1.a1.a1
672.400.1b $1$ R \(\Q\) 672.400.1b $C_{24}:D_{14}$ $C_2$ $2$ 2.e1.a1 $336$ 1.a1.a1
672.400.1c $1$ R \(\Q\) 672.400.1c $C_{24}:D_{14}$ $C_2$ $2$ 2.d1.a1 $336$ 1.a1.a1
672.400.1d $1$ R \(\Q\) 672.400.1d $C_{24}:D_{14}$ $C_2$ $2$ 2.b1.b1 $336$ 1.a1.a1
672.400.1e $1$ R \(\Q\) 672.400.1e $C_{24}:D_{14}$ $C_2$ $2$ 2.a1.b1 $336$ 1.a1.a1
672.400.1f $1$ R \(\Q\) 672.400.1f $C_{24}:D_{14}$ $C_2$ $2$ 2.b1.a1 $336$ 1.a1.a1
672.400.1g $1$ R \(\Q\) 672.400.1g $C_{24}:D_{14}$ $C_2$ $2$ 2.a1.a1 $336$ 1.a1.a1
672.400.1h $1$ R \(\Q\) 672.400.1h $C_{24}:D_{14}$ $C_2$ $2$ 2.c1.a1 $336$ 1.a1.a1
672.400.2a $2$ R \(\Q\) 672.400.2a $C_{24}:D_{14}$ $S_3$ $6$ 6.a1.a1 $112$ 6.a1.a1
672.400.2b $2$ R \(\Q\) 672.400.2b $C_{24}:D_{14}$ $D_4$ $8$ 8.c1.a1 $84$ 4.b1.a1
672.400.2c $2$ R \(\Q\) 672.400.2c $C_{24}:D_{14}$ $D_4$ $8$ 8.a1.a1 $84$ 4.b1.a1
672.400.2d $2$ R \(\Q\) 672.400.2d $C_{24}:D_{14}$ $D_6$ $12$ 12.b1.a1 $56$ 6.a1.a1
672.400.2e $2$ R \(\Q\) 672.400.2e $C_{24}:D_{14}$ $D_6$ $12$ 12.a1.b1 $56$ 6.a1.a1
672.400.2f $2$ R \(\Q\) 672.400.2f $C_{24}:D_{14}$ $D_6$ $12$ 12.a1.a1 $56$ 6.a1.a1
672.400.2g1 $2$ R \(\Q(\sqrt{2}) \) 672.400.2g $C_{24}:D_{14}$ $D_8$ $16$ 16.b1.b1 $42$ 8.a1.a1
672.400.2g2 $2$ R \(\Q(\sqrt{2}) \) 672.400.2g $C_{24}:D_{14}$ $D_8$ $16$ 16.b1.b1 $42$ 8.a1.a1
672.400.2h1 $2$ R \(\Q(\sqrt{2}) \) 672.400.2h $C_{24}:D_{14}$ $D_8$ $16$ 16.b1.a1 $42$ 8.a1.a1
672.400.2h2 $2$ R \(\Q(\sqrt{2}) \) 672.400.2h $C_{24}:D_{14}$ $D_8$ $16$ 16.b1.a1 $42$ 8.a1.a1
672.400.2i1 $2$ R \(\Q(\zeta_{7})^+\) 672.400.2i $C_{24}:D_{14}$ $D_7$ $14$ 14.a1.a1 $48$ 14.a1.a1
672.400.2i2 $2$ R \(\Q(\zeta_{7})^+\) 672.400.2i $C_{24}:D_{14}$ $D_7$ $14$ 14.a1.a1 $48$ 14.a1.a1
672.400.2i3 $2$ R \(\Q(\zeta_{7})^+\) 672.400.2i $C_{24}:D_{14}$ $D_7$ $14$ 14.a1.a1 $48$ 14.a1.a1
672.400.2j1 $2$ R \(\Q(\zeta_{7})^+\) 672.400.2j $C_{24}:D_{14}$ $D_{14}$ $28$ 28.b1.a1 $24$ 14.a1.a1
672.400.2j2 $2$ R \(\Q(\zeta_{7})^+\) 672.400.2j $C_{24}:D_{14}$ $D_{14}$ $28$ 28.b1.a1 $24$ 14.a1.a1
672.400.2j3 $2$ R \(\Q(\zeta_{7})^+\) 672.400.2j $C_{24}:D_{14}$ $D_{14}$ $28$ 28.b1.a1 $24$ 14.a1.a1
672.400.2k1 $2$ R \(\Q(\zeta_{7})^+\) 672.400.2k $C_{24}:D_{14}$ $D_{14}$ $28$ 28.a1.b1 $24$ 14.a1.a1
672.400.2k2 $2$ R \(\Q(\zeta_{7})^+\) 672.400.2k $C_{24}:D_{14}$ $D_{14}$ $28$ 28.a1.b1 $24$ 14.a1.a1
672.400.2k3 $2$ R \(\Q(\zeta_{7})^+\) 672.400.2k $C_{24}:D_{14}$ $D_{14}$ $28$ 28.a1.b1 $24$ 14.a1.a1
672.400.2l1 $2$ R \(\Q(\zeta_{7})^+\) 672.400.2l $C_{24}:D_{14}$ $D_{14}$ $28$ 28.a1.a1 $24$ 14.a1.a1
672.400.2l2 $2$ R \(\Q(\zeta_{7})^+\) 672.400.2l $C_{24}:D_{14}$ $D_{14}$ $28$ 28.a1.a1 $24$ 14.a1.a1
672.400.2l3 $2$ R \(\Q(\zeta_{7})^+\) 672.400.2l $C_{24}:D_{14}$ $D_{14}$ $28$ 28.a1.a1 $24$ 14.a1.a1
672.400.4a $4$ R \(\Q\) 672.400.4a $C_{24}:D_{14}$ $S_3\times D_4$ $48$ 48.a1.a1 $14$ 24.a1.a1
672.400.4b1 $4$ R \(\Q(\sqrt{2}) \) 672.400.4b $C_{24}:D_{14}$ $S_3\times D_8$ $96$ 96.a1.a1 $7$ 48.a1.a1
672.400.4b2 $4$ R \(\Q(\sqrt{2}) \) 672.400.4b $C_{24}:D_{14}$ $S_3\times D_8$ $96$ 96.a1.a1 $7$ 48.a1.a1
672.400.4c1 $4$ R \(\Q(\zeta_{7})^+\) 672.400.4c $C_{24}:D_{14}$ $S_3\times D_7$ $84$ 84.a1.a1 $8$ 84.a1.a1
672.400.4c2 $4$ R \(\Q(\zeta_{7})^+\) 672.400.4c $C_{24}:D_{14}$ $S_3\times D_7$ $84$ 84.a1.a1 $8$ 84.a1.a1
672.400.4c3 $4$ R \(\Q(\zeta_{7})^+\) 672.400.4c $C_{24}:D_{14}$ $S_3\times D_7$ $84$ 84.a1.a1 $8$ 84.a1.a1
672.400.4d1 $4$ R \(\Q(\zeta_{7})^+\) 672.400.4d $C_{24}:D_{14}$ $D_4\times D_7$ $112$ 112.a1.a1 $6$ 56.a1.a1
672.400.4d2 $4$ R \(\Q(\zeta_{7})^+\) 672.400.4d $C_{24}:D_{14}$ $D_4\times D_7$ $112$ 112.a1.a1 $6$ 56.a1.a1
672.400.4d3 $4$ R \(\Q(\zeta_{7})^+\) 672.400.4d $C_{24}:D_{14}$ $D_4\times D_7$ $112$ 112.a1.a1 $6$ 56.a1.a1
672.400.4e1 $4$ R \(\Q(\zeta_{7})^+\) 672.400.4e $C_{24}:D_{14}$ $S_3\times D_{14}$ $168$ 168.a1.a1 $4$ 84.a1.a1
672.400.4e2 $4$ R \(\Q(\zeta_{7})^+\) 672.400.4e $C_{24}:D_{14}$ $S_3\times D_{14}$ $168$ 168.a1.a1 $4$ 84.a1.a1
672.400.4e3 $4$ R \(\Q(\zeta_{7})^+\) 672.400.4e $C_{24}:D_{14}$ $S_3\times D_{14}$ $168$ 168.a1.a1 $4$ 84.a1.a1
672.400.4f1 $4$ R 6.6.1229312.1 672.400.4f $C_{24}:D_{14}$ $D_7\times D_8$ $224$ 224.a1.a1 $3$ 112.a1.a1
672.400.4f2 $4$ R 6.6.1229312.1 672.400.4f $C_{24}:D_{14}$ $D_7\times D_8$ $224$ 224.a1.a1 $3$ 112.a1.a1
672.400.4f3 $4$ R 6.6.1229312.1 672.400.4f $C_{24}:D_{14}$ $D_7\times D_8$ $224$ 224.a1.a1 $3$ 112.a1.a1
672.400.4f4 $4$ R 6.6.1229312.1 672.400.4f $C_{24}:D_{14}$ $D_7\times D_8$ $224$ 224.a1.a1 $3$ 112.a1.a1
672.400.4f5 $4$ R 6.6.1229312.1 672.400.4f $C_{24}:D_{14}$ $D_7\times D_8$ $224$ 224.a1.a1 $3$ 112.a1.a1
672.400.4f6 $4$ R 6.6.1229312.1 672.400.4f $C_{24}:D_{14}$ $D_7\times D_8$ $224$ 224.a1.a1 $3$ 112.a1.a1
672.400.4g1 $4$ C 6.0.29042496.1 672.400.4g $C_{24}:D_{14}$ $C_{12}:D_{14}$ $336$ 336.a1.a1 $2$ 168.a1.a1
672.400.4g2 $4$ C 6.0.29042496.1 672.400.4g $C_{24}:D_{14}$ $C_{12}:D_{14}$ $336$ 336.a1.a1 $2$ 168.a1.a1
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