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Label Degree Type Faithful Field of Traces $\Q$-character Group Image Image Order Kernel Kernel Order Center
224.50.1a $1$ R \(\Q\) 224.50.1a $C_{28}.D_4$ $C_1$ $1$ 1.a1.a1 $224$ 1.a1.a1
224.50.1b $1$ R \(\Q\) 224.50.1b $C_{28}.D_4$ $C_2$ $2$ 2.b1.a1 $112$ 1.a1.a1
224.50.1c $1$ R \(\Q\) 224.50.1c $C_{28}.D_4$ $C_2$ $2$ 2.b1.b1 $112$ 1.a1.a1
224.50.1d $1$ R \(\Q\) 224.50.1d $C_{28}.D_4$ $C_2$ $2$ 2.a1.a1 $112$ 1.a1.a1
224.50.1e1 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1e $C_{28}.D_4$ $C_4$ $4$ 4.b1.b1 $56$ 1.a1.a1
224.50.1e2 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1e $C_{28}.D_4$ $C_4$ $4$ 4.b1.b1 $56$ 1.a1.a1
224.50.1f1 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1f $C_{28}.D_4$ $C_4$ $4$ 4.b1.a1 $56$ 1.a1.a1
224.50.1f2 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1f $C_{28}.D_4$ $C_4$ $4$ 4.b1.a1 $56$ 1.a1.a1
224.50.1g1 $1$ C \(\Q(\zeta_{7})\) 224.50.1g $C_{28}.D_4$ $C_7$ $7$ 7.a1.a1 $32$ 1.a1.a1
224.50.1g2 $1$ C \(\Q(\zeta_{7})\) 224.50.1g $C_{28}.D_4$ $C_7$ $7$ 7.a1.a1 $32$ 1.a1.a1
224.50.1g3 $1$ C \(\Q(\zeta_{7})\) 224.50.1g $C_{28}.D_4$ $C_7$ $7$ 7.a1.a1 $32$ 1.a1.a1
224.50.1g4 $1$ C \(\Q(\zeta_{7})\) 224.50.1g $C_{28}.D_4$ $C_7$ $7$ 7.a1.a1 $32$ 1.a1.a1
224.50.1g5 $1$ C \(\Q(\zeta_{7})\) 224.50.1g $C_{28}.D_4$ $C_7$ $7$ 7.a1.a1 $32$ 1.a1.a1
224.50.1g6 $1$ C \(\Q(\zeta_{7})\) 224.50.1g $C_{28}.D_4$ $C_7$ $7$ 7.a1.a1 $32$ 1.a1.a1
224.50.1h1 $1$ C \(\Q(\zeta_{7})\) 224.50.1h $C_{28}.D_4$ $C_{14}$ $14$ 14.b1.a1 $16$ 1.a1.a1
224.50.1h2 $1$ C \(\Q(\zeta_{7})\) 224.50.1h $C_{28}.D_4$ $C_{14}$ $14$ 14.b1.a1 $16$ 1.a1.a1
224.50.1h3 $1$ C \(\Q(\zeta_{7})\) 224.50.1h $C_{28}.D_4$ $C_{14}$ $14$ 14.b1.a1 $16$ 1.a1.a1
224.50.1h4 $1$ C \(\Q(\zeta_{7})\) 224.50.1h $C_{28}.D_4$ $C_{14}$ $14$ 14.b1.a1 $16$ 1.a1.a1
224.50.1h5 $1$ C \(\Q(\zeta_{7})\) 224.50.1h $C_{28}.D_4$ $C_{14}$ $14$ 14.b1.a1 $16$ 1.a1.a1
224.50.1h6 $1$ C \(\Q(\zeta_{7})\) 224.50.1h $C_{28}.D_4$ $C_{14}$ $14$ 14.b1.a1 $16$ 1.a1.a1
224.50.1i1 $1$ C \(\Q(\zeta_{7})\) 224.50.1i $C_{28}.D_4$ $C_{14}$ $14$ 14.b1.b1 $16$ 1.a1.a1
224.50.1i2 $1$ C \(\Q(\zeta_{7})\) 224.50.1i $C_{28}.D_4$ $C_{14}$ $14$ 14.b1.b1 $16$ 1.a1.a1
224.50.1i3 $1$ C \(\Q(\zeta_{7})\) 224.50.1i $C_{28}.D_4$ $C_{14}$ $14$ 14.b1.b1 $16$ 1.a1.a1
224.50.1i4 $1$ C \(\Q(\zeta_{7})\) 224.50.1i $C_{28}.D_4$ $C_{14}$ $14$ 14.b1.b1 $16$ 1.a1.a1
224.50.1i5 $1$ C \(\Q(\zeta_{7})\) 224.50.1i $C_{28}.D_4$ $C_{14}$ $14$ 14.b1.b1 $16$ 1.a1.a1
224.50.1i6 $1$ C \(\Q(\zeta_{7})\) 224.50.1i $C_{28}.D_4$ $C_{14}$ $14$ 14.b1.b1 $16$ 1.a1.a1
224.50.1j1 $1$ C \(\Q(\zeta_{7})\) 224.50.1j $C_{28}.D_4$ $C_{14}$ $14$ 14.a1.a1 $16$ 1.a1.a1
224.50.1j2 $1$ C \(\Q(\zeta_{7})\) 224.50.1j $C_{28}.D_4$ $C_{14}$ $14$ 14.a1.a1 $16$ 1.a1.a1
224.50.1j3 $1$ C \(\Q(\zeta_{7})\) 224.50.1j $C_{28}.D_4$ $C_{14}$ $14$ 14.a1.a1 $16$ 1.a1.a1
224.50.1j4 $1$ C \(\Q(\zeta_{7})\) 224.50.1j $C_{28}.D_4$ $C_{14}$ $14$ 14.a1.a1 $16$ 1.a1.a1
224.50.1j5 $1$ C \(\Q(\zeta_{7})\) 224.50.1j $C_{28}.D_4$ $C_{14}$ $14$ 14.a1.a1 $16$ 1.a1.a1
224.50.1j6 $1$ C \(\Q(\zeta_{7})\) 224.50.1j $C_{28}.D_4$ $C_{14}$ $14$ 14.a1.a1 $16$ 1.a1.a1
224.50.1k1 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1k $C_{28}.D_4$ $C_{28}$ $28$ 28.b1.b1 $8$ 1.a1.a1
224.50.1k10 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1k $C_{28}.D_4$ $C_{28}$ $28$ 28.b1.b1 $8$ 1.a1.a1
224.50.1k11 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1k $C_{28}.D_4$ $C_{28}$ $28$ 28.b1.b1 $8$ 1.a1.a1
224.50.1k12 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1k $C_{28}.D_4$ $C_{28}$ $28$ 28.b1.b1 $8$ 1.a1.a1
224.50.1k2 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1k $C_{28}.D_4$ $C_{28}$ $28$ 28.b1.b1 $8$ 1.a1.a1
224.50.1k3 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1k $C_{28}.D_4$ $C_{28}$ $28$ 28.b1.b1 $8$ 1.a1.a1
224.50.1k4 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1k $C_{28}.D_4$ $C_{28}$ $28$ 28.b1.b1 $8$ 1.a1.a1
224.50.1k5 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1k $C_{28}.D_4$ $C_{28}$ $28$ 28.b1.b1 $8$ 1.a1.a1
224.50.1k6 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1k $C_{28}.D_4$ $C_{28}$ $28$ 28.b1.b1 $8$ 1.a1.a1
224.50.1k7 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1k $C_{28}.D_4$ $C_{28}$ $28$ 28.b1.b1 $8$ 1.a1.a1
224.50.1k8 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1k $C_{28}.D_4$ $C_{28}$ $28$ 28.b1.b1 $8$ 1.a1.a1
224.50.1k9 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1k $C_{28}.D_4$ $C_{28}$ $28$ 28.b1.b1 $8$ 1.a1.a1
224.50.1l1 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1l $C_{28}.D_4$ $C_{28}$ $28$ 28.b1.a1 $8$ 1.a1.a1
224.50.1l10 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1l $C_{28}.D_4$ $C_{28}$ $28$ 28.b1.a1 $8$ 1.a1.a1
224.50.1l11 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1l $C_{28}.D_4$ $C_{28}$ $28$ 28.b1.a1 $8$ 1.a1.a1
224.50.1l12 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1l $C_{28}.D_4$ $C_{28}$ $28$ 28.b1.a1 $8$ 1.a1.a1
224.50.1l2 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1l $C_{28}.D_4$ $C_{28}$ $28$ 28.b1.a1 $8$ 1.a1.a1
224.50.1l3 $1$ C \(\Q(\sqrt{-1}) \) 224.50.1l $C_{28}.D_4$ $C_{28}$ $28$ 28.b1.a1 $8$ 1.a1.a1
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