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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 (7 matches)

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Label	Name	Degree	Order	Parity	Solvable	Nil. class	$\#\Aut(F/K)$	Transitivity	Conj. classes	Subfields	Low Degree Siblings
7T1	$C_7$	$7$	$7$	$1$	✓	$1$	$7$	$1$	$7$
7T2	$D_{7}$	$7$	$14$	$-1$	✓	$-1$	$1$	$1$	$5$		14T2
7T3	$C_7:C_3$	$7$	$21$	$1$	✓	$-1$	$1$	$1$	$5$		21T2
7T4	$F_7$	$7$	$42$	$-1$	✓	$-1$	$1$	$2$	$7$		14T4, 21T4, 42T4
7T5	$\GL(3,2)$	$7$	$168$	$1$		$-1$	$1$	$2$	$6$		7T5, 8T37, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38 x 2
7T6	$A_7$	$7$	$2520$	$1$		$-1$	$1$	$5$	$9$		15T47 x 2, 21T33, 35T28, 42T294, 42T299
7T7	$S_7$	$7$	$5040$	$-1$		$-1$	$1$	$7$	$15$		14T46, 21T38, 30T565, 35T31, 42T411, 42T412, 42T413, 42T418

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