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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 (12 matches)

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Label	Name	Degree	Order	Parity	Solvable	Nil. class	$\#\Aut(F/K)$	Transitivity	Conj. classes	Subfields	Low Degree Siblings
31T1	$C_{31}$	$31$	$31$	$1$	✓	$1$	$31$	$1$	$31$
31T2	$D_{31}$	$31$	$62$	$-1$	✓	$-1$	$1$	$1$	$17$
31T3	$C_{31}:C_{3}$	$31$	$93$	$1$	✓	$-1$	$1$	$1$	$13$
31T4	$C_{31}:C_{5}$	$31$	$155$	$1$	✓	$-1$	$1$	$1$	$11$
31T5	$C_{31}:C_{6}$	$31$	$186$	$-1$	✓	$-1$	$1$	$1$	$11$
31T6	$C_{31}:C_{10}$	$31$	$310$	$-1$	✓	$-1$	$1$	$1$	$13$
31T7	$C_{31}:C_{15}$	$31$	$465$	$1$	✓	$-1$	$1$	$1$	$17$
31T8	$F_{31}$	$31$	$930$	$-1$	✓	$-1$	$1$	$2$	$31$
31T9	$\PSL(3,5)$	$31$	$372000$	$1$		$-1$	$1$	$2$	$30$		31T9
31T10	$\PSL(5,2)$	$31$	$9999360$	$1$		$-1$	$1$	$2$	$27$		31T10
31T11	$A_{31}$	$31$	$4111419327088961408862781440000000$	$1$		$-1$	$1$	$29$	$3451$
31T12	$S_{31}$	$31$	$8222838654177922817725562880000000$	$-1$		$-1$	$1$	$31$	$6842$

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