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The results below are complete, since the LMFDB contains all transitive groups of degree at most 47 (except 32)

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Parity	Cyclic	Solvable	Primitive	Equivalent siblings

Degree	$T$-number	Order	Group	Nilpotency class

$\#\Aut(F/K)$	Transitivity

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Results (10 matches)

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Label	Name	Degree	Order	Parity	Solvable	Nil. class	$\#\Aut(F/K)$	Transitivity	Conj. classes	Subfields	Low Degree Siblings
17T1	$C_{17}$	$17$	$17$	$1$	✓	$1$	$17$	$1$	$17$
17T2	$D_{17}$	$17$	$34$	$1$	✓	$-1$	$1$	$1$	$10$
17T3	$C_{17}:C_{4}$	$17$	$68$	$1$	✓	$-1$	$1$	$1$	$8$
17T4	$C_{17}:C_{8}$	$17$	$136$	$1$	✓	$-1$	$1$	$1$	$10$
17T5	$F_{17}$	$17$	$272$	$-1$	✓	$-1$	$1$	$2$	$17$
17T6	$\PSL(2,16)$	$17$	$4080$	$1$		$-1$	$1$	$3$	$17$
17T7	$\PSL(2,16):C_2$	$17$	$8160$	$1$		$-1$	$1$	$3$	$16$
17T8	$\PSL(2,16):C_4$	$17$	$16320$	$1$		$-1$	$1$	$3$	$17$
17T9	$A_{17}$	$17$	$177843714048000$	$1$		$-1$	$1$	$15$	$156$
17T10	$S_{17}$	$17$	$355687428096000$	$-1$		$-1$	$1$	$17$	$297$

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