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Parity Cyclic Solvable Primitive Equivalent siblings
Degree $T$-number Order Group Nilpotency class
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Results (14 matches)

  displayed columns for results
Label Name Order Parity Solvable Subfields Low Degree Siblings
12T172 $C_3^4:D_4$ $648$ $1$ ✓ $C_2$ x 3, $C_2^2$ 12T172 x 5, 18T213 x 2, 18T214 x 3, 18T216 x 12, 24T1524 x 6, 36T1112 x 2, 36T1113 x 2, 36T1114 x 2, 36T1115 x 3, 36T1119 x 12, 36T1120 x 24, 36T1187 x 12, 36T1189 x 8, 36T1234 x 3
18T213 $C_3^4:D_4$ $648$ $-1$ ✓ $C_2$, $C_3^2:D_4$ x 4 12T172 x 6, 18T213, 18T214 x 3, 18T216 x 12, 24T1524 x 6, 36T1112 x 2, 36T1113 x 2, 36T1114 x 2, 36T1115 x 3, 36T1119 x 12, 36T1120 x 24, 36T1187 x 12, 36T1189 x 8, 36T1234 x 3
18T214 $C_3^4:D_4$ $648$ $-1$ ✓ $C_2$ 12T172 x 6, 18T213 x 2, 18T214 x 2, 18T216 x 12, 24T1524 x 6, 36T1112 x 2, 36T1113 x 2, 36T1114 x 2, 36T1115 x 3, 36T1119 x 12, 36T1120 x 24, 36T1187 x 12, 36T1189 x 8, 36T1234 x 3
18T216 $C_3^4:D_4$ $648$ $-1$ ✓ $C_2$, $C_3^2:D_4$ x 2 12T172 x 6, 18T213 x 2, 18T214 x 3, 18T216 x 11, 24T1524 x 6, 36T1112 x 2, 36T1113 x 2, 36T1114 x 2, 36T1115 x 3, 36T1119 x 12, 36T1120 x 24, 36T1187 x 12, 36T1189 x 8, 36T1234 x 3
24T1524 $C_3^4:D_4$ $648$ $1$ ✓ $C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $C_3^4:D_4$ 12T172 x 6, 18T213 x 2, 18T214 x 3, 18T216 x 12, 24T1524 x 5, 36T1112 x 2, 36T1113 x 2, 36T1114 x 2, 36T1115 x 3, 36T1119 x 12, 36T1120 x 24, 36T1187 x 12, 36T1189 x 8, 36T1234 x 3
36T1112 $C_3^4:D_4$ $648$ $-1$ ✓ $C_2$, $D_{4}$, $C_3^2:D_4$ x 4, $\SOPlus(4,2)$ x 4, $C_3^4:D_4$ 12T172 x 6, 18T213 x 2, 18T214 x 3, 18T216 x 12, 24T1524 x 6, 36T1112, 36T1113 x 2, 36T1114 x 2, 36T1115 x 3, 36T1119 x 12, 36T1120 x 24, 36T1187 x 12, 36T1189 x 8, 36T1234 x 3
36T1113 $C_3^4:D_4$ $648$ $1$ ✓ $C_2$ x 3, $C_2^2$, $C_3^2:D_4$ x 4, $\SOPlus(4,2)$ x 4, $C_3^4:D_4$ 12T172 x 6, 18T213 x 2, 18T214 x 3, 18T216 x 12, 24T1524 x 6, 36T1112 x 2, 36T1113, 36T1114 x 2, 36T1115 x 3, 36T1119 x 12, 36T1120 x 24, 36T1187 x 12, 36T1189 x 8, 36T1234 x 3
36T1114 $C_3^4:D_4$ $648$ $-1$ ✓ $C_2$, $D_{4}$, $C_3^2:D_4$ x 4, $\SOPlus(4,2)$ x 4, $C_3^4:D_4$ 12T172 x 6, 18T213 x 2, 18T214 x 3, 18T216 x 12, 24T1524 x 6, 36T1112 x 2, 36T1113 x 2, 36T1114, 36T1115 x 3, 36T1119 x 12, 36T1120 x 24, 36T1187 x 12, 36T1189 x 8, 36T1234 x 3
36T1115 $C_3^4:D_4$ $648$ $1$ ✓ $C_2$ x 3, $C_2^2$, $C_3^4:D_4$ x 2, $C_3^4:D_4$ 12T172 x 6, 18T213 x 2, 18T214 x 3, 18T216 x 12, 24T1524 x 6, 36T1112 x 2, 36T1113 x 2, 36T1114 x 2, 36T1115 x 2, 36T1119 x 12, 36T1120 x 24, 36T1187 x 12, 36T1189 x 8, 36T1234 x 3
36T1119 $C_3^4:D_4$ $648$ $1$ ✓ $C_2$ x 3, $C_2^2$, $C_3^2:D_4$ x 2, $\SOPlus(4,2)$ x 2, $C_3^4:D_4$, $C_3^4:D_4$ 12T172 x 6, 18T213 x 2, 18T214 x 3, 18T216 x 12, 24T1524 x 6, 36T1112 x 2, 36T1113 x 2, 36T1114 x 2, 36T1115 x 3, 36T1119 x 11, 36T1120 x 24, 36T1187 x 12, 36T1189 x 8, 36T1234 x 3
36T1120 $C_3^4:D_4$ $648$ $-1$ ✓ $C_2$, $D_{4}$, $C_3^2:D_4$ x 2, $\SOPlus(4,2)$, $\SOPlus(4,2)$, $C_3^4:D_4$ 12T172 x 6, 18T213 x 2, 18T214 x 3, 18T216 x 12, 24T1524 x 6, 36T1112 x 2, 36T1113 x 2, 36T1114 x 2, 36T1115 x 3, 36T1119 x 12, 36T1120 x 23, 36T1187 x 12, 36T1189 x 8, 36T1234 x 3
36T1187 $C_3^4:D_4$ $648$ $1$ ✓ $C_2$ x 3, $C_2^2$, $C_3^2:D_4$ x 2, $\SOPlus(4,2)$ x 2, $C_3^4:D_4$ x 2 12T172 x 6, 18T213 x 2, 18T214 x 3, 18T216 x 12, 24T1524 x 6, 36T1112 x 2, 36T1113 x 2, 36T1114 x 2, 36T1115 x 3, 36T1119 x 12, 36T1120 x 24, 36T1187 x 11, 36T1189 x 8, 36T1234 x 3
36T1189 $C_3^4:D_4$ $648$ $1$ ✓ $C_2$ x 3, $C_2^2$, $C_3^2:D_4$, $\SOPlus(4,2)$, $C_3^4:D_4$ x 3 12T172 x 6, 18T213 x 2, 18T214 x 3, 18T216 x 12, 24T1524 x 6, 36T1112 x 2, 36T1113 x 2, 36T1114 x 2, 36T1115 x 3, 36T1119 x 12, 36T1120 x 24, 36T1187 x 12, 36T1189 x 7, 36T1234 x 3
36T1234 $C_3^4:D_4$ $648$ $1$ ✓ $C_2$ x 3, $C_2^2$, $C_3^4:D_4$ x 4 12T172 x 6, 18T213 x 2, 18T214 x 3, 18T216 x 12, 24T1524 x 6, 36T1112 x 2, 36T1113 x 2, 36T1114 x 2, 36T1115 x 3, 36T1119 x 12, 36T1120 x 24, 36T1187 x 12, 36T1189 x 8, 36T1234 x 2
  displayed columns for results

Results are complete for degrees $\leq 23$.