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Parity	Cyclic	Solvable	Primitive	Equivalent siblings

Degree	$T$-number	Order	Group	Nilpotency class

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Results (4 matches)

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Label	Name	Order	Parity	Solvable	Nil. class	Conj. classes	Subfields	Low Degree Siblings
24T1532	$C_3:S_3^3$	$648$	$1$	✓	$-1$	$45$	$C_2$ x 7, $C_2^2$ x 7, $C_2^3$	36T1136 x 3, 36T1143, 36T1174 x 3
36T1136	$C_3:S_3^3$	$648$	$1$	✓	$-1$	$45$	$C_2$ x 3, $S_3$, $C_2^2$, $S_3$, $D_{6}$ x 2, $D_6$, $S_3^3$	24T1532, 36T1136 x 2, 36T1143, 36T1174 x 3
36T1143	$C_3:S_3^3$	$648$	$1$	✓	$-1$	$45$	$C_2$ x 3, $S_3$, $C_2^2$, $D_{6}$ x 3, $S_3 \times C_2^2$, $C_3:S_3^2$	24T1532, 36T1136 x 3, 36T1174 x 3
36T1174	$C_3:S_3^3$	$648$	$1$	✓	$-1$	$45$	$C_2$ x 3, $C_2^2$, $S_3^2$ x 2, $S_3^2$, $S_3\times D_6$	24T1532, 36T1136 x 3, 36T1143, 36T1174 x 2

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Results are complete for degrees $\leq 23$.