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The results below are complete, since the LMFDB contains all groups acting as automorphisms of curves of genus 2, 3 or 4

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Genus Dimension of the family Group order Hyperelliptic curves Full automorphism group
Quotient genus Signature Group identifier Cyclic trigonal curves
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Results (8 matches)

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Refined passport label Genus Group Group order Dimension Signature Generating vectors
3.16-11.0.2-2-2-4.2 $3$ $C_2\times D_4$ $16$ $1$ $[ 0; 2, 2, 2, 4 ]$ $(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
3.16-11.0.2-2-2-4.3 $3$ $C_2\times D_4$ $16$ $1$ $[ 0; 2, 2, 2, 4 ]$ $(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
3.16-11.0.2-2-2-4.4 $3$ $C_2\times D_4$ $16$ $1$ $[ 0; 2, 2, 2, 4 ]$ $(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
3.16-11.0.2-2-2-4.6 $3$ $C_2\times D_4$ $16$ $1$ $[ 0; 2, 2, 2, 4 ]$ $(1,4)(2,3)(5,8)(6,7)(9,12)(10,11)(13,16)(14,15),\ldots$
3.16-11.0.2-2-2-4.7 $3$ $C_2\times D_4$ $16$ $1$ $[ 0; 2, 2, 2, 4 ]$ $(1,4)(2,3)(5,8)(6,7)(9,12)(10,11)(13,16)(14,15),\ldots$
3.16-11.0.2-2-2-4.8 $3$ $C_2\times D_4$ $16$ $1$ $[ 0; 2, 2, 2, 4 ]$ $(1,4)(2,3)(5,8)(6,7)(9,12)(10,11)(13,16)(14,15),\ldots$
3.16-11.0.2-2-2-4.5 $3$ $C_2\times D_4$ $16$ $1$ $[ 0; 2, 2, 2, 4 ]$ $(1,4)(2,3)(5,8)(6,7)(9,12)(10,11)(13,16)(14,15),\ldots$
3.16-11.0.2-2-2-4.1 $3$ $C_2\times D_4$ $16$ $1$ $[ 0; 2, 2, 2, 4 ]$ $(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(13,15)(14,16),\ldots$
  displayed columns for results