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Label Degree Type Faithful Field of Traces $\Q$-character Group Image Image Order Kernel Kernel Order Center
224.137.1a $1$ R \(\Q\) 224.137.1a $C_{28}.D_4$ $C_1$ $1$ 1.a1.a1 $224$ 1.a1.a1
224.137.1b $1$ R \(\Q\) 224.137.1b $C_{28}.D_4$ $C_2$ $2$ 2.e1.b1 $112$ 1.a1.a1
224.137.1c $1$ R \(\Q\) 224.137.1c $C_{28}.D_4$ $C_2$ $2$ 2.e1.a1 $112$ 1.a1.a1
224.137.1d $1$ R \(\Q\) 224.137.1d $C_{28}.D_4$ $C_2$ $2$ 2.d1.b1 $112$ 1.a1.a1
224.137.1e $1$ R \(\Q\) 224.137.1e $C_{28}.D_4$ $C_2$ $2$ 2.d1.a1 $112$ 1.a1.a1
224.137.1f $1$ R \(\Q\) 224.137.1f $C_{28}.D_4$ $C_2$ $2$ 2.c1.a1 $112$ 1.a1.a1
224.137.1g $1$ R \(\Q\) 224.137.1g $C_{28}.D_4$ $C_2$ $2$ 2.b1.a1 $112$ 1.a1.a1
224.137.1h $1$ R \(\Q\) 224.137.1h $C_{28}.D_4$ $C_2$ $2$ 2.a1.a1 $112$ 1.a1.a1
224.137.2a $2$ R \(\Q\) 224.137.2a $C_{28}.D_4$ $D_4$ $8$ 8.b1.a1 $28$ 4.a1.a1
224.137.2b $2$ R \(\Q\) 224.137.2b $C_{28}.D_4$ $D_4$ $8$ 8.a1.a1 $28$ 4.a1.a1
224.137.2c1 $2$ R \(\Q(\zeta_{7})^+\) 224.137.2c $C_{28}.D_4$ $D_7$ $14$ 14.a1.a1 $16$ 14.a1.a1
224.137.2c2 $2$ R \(\Q(\zeta_{7})^+\) 224.137.2c $C_{28}.D_4$ $D_7$ $14$ 14.a1.a1 $16$ 14.a1.a1
224.137.2c3 $2$ R \(\Q(\zeta_{7})^+\) 224.137.2c $C_{28}.D_4$ $D_7$ $14$ 14.a1.a1 $16$ 14.a1.a1
224.137.2d1 $2$ R \(\Q(\zeta_{7})^+\) 224.137.2d $C_{28}.D_4$ $D_{14}$ $28$ 28.b1.b1 $8$ 14.a1.a1
224.137.2d2 $2$ R \(\Q(\zeta_{7})^+\) 224.137.2d $C_{28}.D_4$ $D_{14}$ $28$ 28.b1.b1 $8$ 14.a1.a1
224.137.2d3 $2$ R \(\Q(\zeta_{7})^+\) 224.137.2d $C_{28}.D_4$ $D_{14}$ $28$ 28.b1.b1 $8$ 14.a1.a1
224.137.2e1 $2$ R \(\Q(\zeta_{7})^+\) 224.137.2e $C_{28}.D_4$ $D_{14}$ $28$ 28.b1.a1 $8$ 14.a1.a1
224.137.2e2 $2$ R \(\Q(\zeta_{7})^+\) 224.137.2e $C_{28}.D_4$ $D_{14}$ $28$ 28.b1.a1 $8$ 14.a1.a1
224.137.2e3 $2$ R \(\Q(\zeta_{7})^+\) 224.137.2e $C_{28}.D_4$ $D_{14}$ $28$ 28.b1.a1 $8$ 14.a1.a1
224.137.2f1 $2$ R \(\Q(\zeta_{7})^+\) 224.137.2f $C_{28}.D_4$ $D_{14}$ $28$ 28.a1.a1 $8$ 14.a1.a1
224.137.2f2 $2$ R \(\Q(\zeta_{7})^+\) 224.137.2f $C_{28}.D_4$ $D_{14}$ $28$ 28.a1.a1 $8$ 14.a1.a1
224.137.2f3 $2$ R \(\Q(\zeta_{7})^+\) 224.137.2f $C_{28}.D_4$ $D_{14}$ $28$ 28.a1.a1 $8$ 14.a1.a1
224.137.2g1 $2$ C \(\Q(\zeta_{7})\) 224.137.2g $C_{28}.D_4$ $C_7:D_4$ $56$ 56.b1.a1 $4$ 28.a1.a1
224.137.2g2 $2$ C \(\Q(\zeta_{7})\) 224.137.2g $C_{28}.D_4$ $C_7:D_4$ $56$ 56.b1.a1 $4$ 28.a1.a1
224.137.2g3 $2$ C \(\Q(\zeta_{7})\) 224.137.2g $C_{28}.D_4$ $C_7:D_4$ $56$ 56.b1.a1 $4$ 28.a1.a1
224.137.2g4 $2$ C \(\Q(\zeta_{7})\) 224.137.2g $C_{28}.D_4$ $C_7:D_4$ $56$ 56.b1.a1 $4$ 28.a1.a1
224.137.2g5 $2$ C \(\Q(\zeta_{7})\) 224.137.2g $C_{28}.D_4$ $C_7:D_4$ $56$ 56.b1.a1 $4$ 28.a1.a1
224.137.2g6 $2$ C \(\Q(\zeta_{7})\) 224.137.2g $C_{28}.D_4$ $C_7:D_4$ $56$ 56.b1.a1 $4$ 28.a1.a1
224.137.2h1 $2$ C \(\Q(\zeta_{7})\) 224.137.2h $C_{28}.D_4$ $C_7:D_4$ $56$ 56.a1.a1 $4$ 28.a1.a1
224.137.2h2 $2$ C \(\Q(\zeta_{7})\) 224.137.2h $C_{28}.D_4$ $C_7:D_4$ $56$ 56.a1.a1 $4$ 28.a1.a1
224.137.2h3 $2$ C \(\Q(\zeta_{7})\) 224.137.2h $C_{28}.D_4$ $C_7:D_4$ $56$ 56.a1.a1 $4$ 28.a1.a1
224.137.2h4 $2$ C \(\Q(\zeta_{7})\) 224.137.2h $C_{28}.D_4$ $C_7:D_4$ $56$ 56.a1.a1 $4$ 28.a1.a1
224.137.2h5 $2$ C \(\Q(\zeta_{7})\) 224.137.2h $C_{28}.D_4$ $C_7:D_4$ $56$ 56.a1.a1 $4$ 28.a1.a1
224.137.2h6 $2$ C \(\Q(\zeta_{7})\) 224.137.2h $C_{28}.D_4$ $C_7:D_4$ $56$ 56.a1.a1 $4$ 28.a1.a1
224.137.4a $4$ S \(\Q\) 224.137.4a $C_{28}.D_4$ $Q_{16}:C_2$ $32$ 32.a1.a1 $7$ 16.a1.a1
224.137.4b1 $4$ C \(\Q(\zeta_{7})\) 224.137.4b $C_{28}.D_4$ $C_{28}.D_4$ $224$ 224.a1.a1 $1$ 112.a1.a1
224.137.4b2 $4$ C \(\Q(\zeta_{7})\) 224.137.4b $C_{28}.D_4$ $C_{28}.D_4$ $224$ 224.a1.a1 $1$ 112.a1.a1
224.137.4b3 $4$ C \(\Q(\zeta_{7})\) 224.137.4b $C_{28}.D_4$ $C_{28}.D_4$ $224$ 224.a1.a1 $1$ 112.a1.a1
224.137.4b4 $4$ C \(\Q(\zeta_{7})\) 224.137.4b $C_{28}.D_4$ $C_{28}.D_4$ $224$ 224.a1.a1 $1$ 112.a1.a1
224.137.4b5 $4$ C \(\Q(\zeta_{7})\) 224.137.4b $C_{28}.D_4$ $C_{28}.D_4$ $224$ 224.a1.a1 $1$ 112.a1.a1
224.137.4b6 $4$ C \(\Q(\zeta_{7})\) 224.137.4b $C_{28}.D_4$ $C_{28}.D_4$ $224$ 224.a1.a1 $1$ 112.a1.a1
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