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Label Degree Type Faithful Field of Traces $\Q$-character Group Image Image Order Kernel Kernel Order Center
30.1.1a $1$ R \(\Q\) 30.1.1a $C_5\times S_3$ $C_1$ $1$ 1.a1.a1 $30$ 1.a1.a1
30.1.1b $1$ R \(\Q\) 30.1.1b $C_5\times S_3$ $C_2$ $2$ 2.a1.a1 $15$ 1.a1.a1
30.1.1c1 $1$ C \(\Q(\zeta_{5})\) 30.1.1c $C_5\times S_3$ $C_5$ $5$ 5.a1.a1 $6$ 1.a1.a1
30.1.1c2 $1$ C \(\Q(\zeta_{5})\) 30.1.1c $C_5\times S_3$ $C_5$ $5$ 5.a1.a1 $6$ 1.a1.a1
30.1.1c3 $1$ C \(\Q(\zeta_{5})\) 30.1.1c $C_5\times S_3$ $C_5$ $5$ 5.a1.a1 $6$ 1.a1.a1
30.1.1c4 $1$ C \(\Q(\zeta_{5})\) 30.1.1c $C_5\times S_3$ $C_5$ $5$ 5.a1.a1 $6$ 1.a1.a1
30.1.1d1 $1$ C \(\Q(\zeta_{5})\) 30.1.1d $C_5\times S_3$ $C_{10}$ $10$ 10.a1.a1 $3$ 1.a1.a1
30.1.1d2 $1$ C \(\Q(\zeta_{5})\) 30.1.1d $C_5\times S_3$ $C_{10}$ $10$ 10.a1.a1 $3$ 1.a1.a1
30.1.1d3 $1$ C \(\Q(\zeta_{5})\) 30.1.1d $C_5\times S_3$ $C_{10}$ $10$ 10.a1.a1 $3$ 1.a1.a1
30.1.1d4 $1$ C \(\Q(\zeta_{5})\) 30.1.1d $C_5\times S_3$ $C_{10}$ $10$ 10.a1.a1 $3$ 1.a1.a1
30.1.2a $2$ R \(\Q\) 30.1.2a $C_5\times S_3$ $S_3$ $6$ 6.a1.a1 $5$ 6.a1.a1
30.1.2b1 $2$ C \(\Q(\zeta_{5})\) 30.1.2b $C_5\times S_3$ $C_5\times S_3$ $30$ 30.a1.a1 $1$ 6.a1.a1
30.1.2b2 $2$ C \(\Q(\zeta_{5})\) 30.1.2b $C_5\times S_3$ $C_5\times S_3$ $30$ 30.a1.a1 $1$ 6.a1.a1
30.1.2b3 $2$ C \(\Q(\zeta_{5})\) 30.1.2b $C_5\times S_3$ $C_5\times S_3$ $30$ 30.a1.a1 $1$ 6.a1.a1
30.1.2b4 $2$ C \(\Q(\zeta_{5})\) 30.1.2b $C_5\times S_3$ $C_5\times S_3$ $30$ 30.a1.a1 $1$ 6.a1.a1
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