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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 (9 matches)

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Refined passport label Genus Group Group order Dimension Signature Generating vectors
3.2-1.1.2-2-2-2.1 $3$ $C_2$ $2$ $4$ $[ 1; 2, 2, 2, 2 ]$ $(1,2),\ldots$
3.3-1.1.3-3.1 $3$ $C_3$ $3$ $2$ $[ 1; 3, 3 ]$ $(1,2,3),\ldots$
3.4-2.1.2-2.1 $3$ $C_2^2$ $4$ $2$ $[ 1; 2, 2 ]$ $(1,2)(3,4),\ldots$
3.4-2.1.2-2.2 $3$ $C_2^2$ $4$ $2$ $[ 1; 2, 2 ]$ $(1,2)(3,4),\ldots$
3.4-1.1.2-2.1 $3$ $C_4$ $4$ $2$ $[ 1; 2, 2 ]$ $(1,2)(3,4),\ldots$
3.4-2.1.2-2.3 $3$ $C_2^2$ $4$ $2$ $[ 1; 2, 2 ]$ $(1,2)(3,4),\ldots$
3.6-1.1.3.1 $3$ $S_3$ $6$ $1$ $[ 1; 3 ]$ $(1,4)(2,6)(3,5),\ldots$
3.8-3.1.2.1 $3$ $D_4$ $8$ $1$ $[ 1; 2 ]$ $(1,5)(2,6)(3,8)(4,7),\ldots$
3.8-4.1.2.1 $3$ $Q_8$ $8$ $1$ $[ 1; 2 ]$ $(1,5,2,6)(3,8,4,7),\ldots$
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