Potentially stably rational conic bundle

This page contains subgroup $G$ of $W(D_7)$ with $H^1(G,Pic(\bar{X}))=0$.

Cases:

• D7(1):$C5:C4$
• D7(2):$D_{10}$
• D7(3):$F_5$
• D7(4):$S_3^2$
• D7(5):$(C_2 \rtimes S_3)\rtimes C_2$
• D7(6):$C_5 \times F_5$
• D7(7):$C_5 \rtimes D_4$
• D7(8):$C_2 \times F_5$
• D7(9):$S_3 \wr C_2$
• D7(10):$C_2^2 \rtimes F_5$