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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
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Results (8 matches)

  displayed columns for results
Label Name Order Parity Solvable Subfields Low Degree Siblings
7T5 $\GL(3,2)$ $168$ $1$ 7T5, 8T37, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38 x 2
8T37 $\PSL(2,7)$ $168$ $1$ 7T5 x 2, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38 x 2
14T10 $\PSL(2,7)$ $168$ $1$ $\GL(3,2)$ 7T5 x 2, 8T37, 14T10, 21T14, 24T284, 28T32, 42T37, 42T38 x 2
21T14 $\PSL(2,7)$ $168$ $1$ $\GL(3,2)$ x 2 7T5 x 2, 8T37, 14T10 x 2, 24T284, 28T32, 42T37, 42T38 x 2
24T284 $\PSL(2,7)$ $168$ $1$ $\PSL(2,7)$ 7T5 x 2, 8T37, 14T10 x 2, 21T14, 28T32, 42T37, 42T38 x 2
28T32 $\PSL(2,7)$ $168$ $1$ $\GL(3,2)$ x 2 7T5 x 2, 8T37, 14T10 x 2, 21T14, 24T284, 42T37, 42T38 x 2
42T37 $\PSL(2,7)$ $168$ $1$ $\GL(3,2)$ x 2, $\PSL(2,7)$ 7T5 x 2, 8T37, 14T10 x 2, 21T14, 24T284, 28T32, 42T38 x 2
42T38 $\PSL(2,7)$ $168$ $1$ $\GL(3,2)$ x 2, $\PSL(2,7)$, $\PSL(2,7)$ 7T5 x 2, 8T37, 14T10 x 2, 21T14, 24T284, 28T32, 42T37, 42T38
  displayed columns for results

Results are complete for degrees $\leq 23$.