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The results below are complete, since the LMFDB contains all Belyi maps of degree at most 6

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Degree Group Orders \([a,b,c]\) triple
Genus Orbit size Passport size Base field
Geometry type Primitive Primitivization
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Results (23 matches)

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Label Degree Group abc Ramification type Genus Orbit Size Base field Triples Primitivization
5T1-5_5_1.1.1.1.1-a $5$ 5T1 $[5, 5, 1]$ $[[5], [5], [1, 1, 1, 1, 1]]$ $0$ $1$ \(\Q\) $[[[2, 3, 4, 5, 1], [5, 1, 2, 3, 4], [1, 2, 3, 4, 5]]]$ 5T1-5_5_1.1.1.1.1-a
5T1-5_5_5-a $5$ 5T1 $[5, 5, 5]$ $[[5], [5], [5]]$ $2$ $1$ \(\Q\) $[[[2, 3, 4, 5, 1], [4, 5, 1, 2, 3], [2, 3, 4, 5, 1]]]$ 5T1-5_5_5-a
5T1-5_5_5-b $5$ 5T1 $[5, 5, 5]$ $[[5], [5], [5]]$ $2$ $1$ \(\Q\) $[[[2, 3, 4, 5, 1], [2, 3, 4, 5, 1], [4, 5, 1, 2, 3]]]$ 5T1-5_5_5-b
5T1-5_5_5-c $5$ 5T1 $[5, 5, 5]$ $[[5], [5], [5]]$ $2$ $1$ \(\Q\) $[[[2, 3, 4, 5, 1], [3, 4, 5, 1, 2], [3, 4, 5, 1, 2]]]$ 5T1-5_5_5-c
5T2-5_2.2.1_2.2.1-a $5$ 5T2 $[5, 2, 2]$ $[[5], [2, 2, 1], [2, 2, 1]]$ $0$ $1$ \(\Q\) $[[[2, 3, 4, 5, 1], [3, 2, 1, 5, 4], [4, 3, 2, 1, 5]]]$ 5T2-5_2.2.1_2.2.1-a
5T3-4.1_4.1_2.2.1-a $5$ 5T3 $[4, 4, 2]$ $[[4, 1], [4, 1], [2, 2, 1]]$ $0$ $2$ \(\Q(\sqrt{-1}) \) $[[[4, 1, 3, 5, 2], [1, 3, 5, 2, 4], [4, 3, 2, 1, 5]], [[2, 5, 3, 1, 4], [5, 3, 1, 4, 2], [4, 3, 2, 1, 5]]]$ 5T3-4.1_4.1_2.2.1-a
5T3-5_4.1_4.1-a $5$ 5T3 $[5, 4, 4]$ $[[5], [4, 1], [4, 1]]$ $1$ $2$ \(\Q(\sqrt{-1}) \) $[[[2, 3, 4, 5, 1], [1, 3, 5, 2, 4], [3, 1, 4, 2, 5]], [[2, 3, 4, 5, 1], [2, 5, 3, 1, 4], [2, 4, 1, 3, 5]]]$ 5T3-5_4.1_4.1-a
5T4-5_2.2.1_3.1.1-a $5$ 5T4 $[5, 2, 3]$ $[[5], [2, 2, 1], [3, 1, 1]]$ $0$ $1$ \(\Q\) $[[[3, 5, 4, 2, 1], [1, 5, 4, 3, 2], [2, 3, 1, 4, 5]]]$ 5T4-5_2.2.1_3.1.1-a
5T4-5_3.1.1_3.1.1-a $5$ 5T4 $[5, 3, 3]$ $[[5], [3, 1, 1], [3, 1, 1]]$ $0$ $1$ \(\Q\) $[[[3, 5, 2, 1, 4], [2, 3, 1, 4, 5], [4, 2, 3, 5, 1]]]$ 5T4-5_3.1.1_3.1.1-a
5T4-5_5_2.2.1-a $5$ 5T4 $[5, 5, 2]$ $[[5], [5], [2, 2, 1]]$ $1$ $1$ \(\Q\) $[[[2, 3, 4, 5, 1], [3, 1, 4, 5, 2], [4, 2, 5, 1, 3]]]$ 5T4-5_5_2.2.1-a
5T4-5_5_3.1.1-a $5$ 5T4 $[5, 5, 3]$ $[[5], [5], [3, 1, 1]]$ $1$ $1$ \(\Q\) $[[[2, 3, 4, 5, 1], [3, 1, 5, 2, 4], [3, 2, 4, 1, 5]]]$ 5T4-5_5_3.1.1-a
5T4-5_5_3.1.1-b $5$ 5T4 $[5, 5, 3]$ $[[5], [5], [3, 1, 1]]$ $1$ $1$ \(\Q\) $[[[2, 3, 4, 5, 1], [5, 1, 4, 2, 3], [1, 2, 4, 5, 3]]]$ 5T4-5_5_3.1.1-b
5T4-5_5_5-a $5$ 5T4 $[5, 5, 5]$ $[[5], [5], [5]]$ $2$ $1$ \(\Q\) $[[[2, 3, 4, 5, 1], [3, 5, 4, 2, 1], [2, 5, 4, 1, 3]]]$ 5T4-5_5_5-a
5T5-3.2_3.2_2.2.1-a $5$ 5T5 $[6, 6, 2]$ $[[3, 2], [3, 2], [2, 2, 1]]$ $0$ $1$ \(\Q\) $[[[2, 3, 1, 5, 4], [5, 1, 4, 3, 2], [4, 2, 5, 1, 3]]]$ 5T5-3.2_3.2_2.2.1-a
5T5-3.2_3.2_3.1.1-a $5$ 5T5 $[6, 6, 3]$ $[[3, 2], [3, 2], [3, 1, 1]]$ $0$ $1$ \(\Q\) $[[[2, 3, 1, 5, 4], [4, 3, 2, 5, 1], [2, 5, 3, 4, 1]]]$ 5T5-3.2_3.2_3.1.1-a
5T5-4.1_2.2.1_3.2-a $5$ 5T5 $[4, 2, 6]$ $[[4, 1], [2, 2, 1], [3, 2]]$ $0$ $1$ \(\Q\) $[[[2, 4, 1, 3, 5], [5, 3, 2, 4, 1], [2, 5, 4, 3, 1]]]$ 5T5-4.1_2.2.1_3.2-a
5T5-4.1_3.2_3.1.1-a $5$ 5T5 $[4, 6, 3]$ $[[4, 1], [3, 2], [3, 1, 1]]$ $0$ $2$ \(\Q(\sqrt{6}) \) $[[[2, 4, 3, 5, 1], [3, 5, 1, 2, 4], [2, 3, 1, 4, 5]], [[4, 2, 5, 3, 1], [4, 5, 2, 1, 3], [2, 3, 1, 4, 5]]]$ 5T5-4.1_3.2_3.1.1-a
5T5-4.1_4.1_3.1.1-a $5$ 5T5 $[4, 4, 3]$ $[[4, 1], [4, 1], [3, 1, 1]]$ $0$ $1$ \(\Q\) $[[[3, 2, 4, 5, 1], [1, 5, 2, 3, 4], [2, 3, 1, 4, 5]]]$ 5T5-4.1_4.1_3.1.1-a
5T5-5_2.1.1.1_3.2-a $5$ 5T5 $[5, 2, 6]$ $[[5], [2, 1, 1, 1], [3, 2]]$ $0$ $1$ \(\Q\) $[[[3, 5, 2, 1, 4], [2, 1, 3, 4, 5], [4, 3, 2, 5, 1]]]$ 5T5-5_2.1.1.1_3.2-a
5T5-5_4.1_2.1.1.1-a $5$ 5T5 $[5, 4, 2]$ $[[5], [4, 1], [2, 1, 1, 1]]$ $0$ $1$ \(\Q\) $[[[2, 3, 4, 5, 1], [1, 5, 2, 3, 4], [2, 1, 3, 4, 5]]]$ 5T5-5_4.1_2.1.1.1-a
5T5-5_3.2_3.2-a $5$ 5T5 $[5, 6, 6]$ $[[5], [3, 2], [3, 2]]$ $1$ $1$ \(\Q\) $[[[4, 5, 1, 2, 3], [2, 3, 1, 5, 4], [2, 5, 4, 3, 1]]]$ 5T5-5_3.2_3.2-a
5T5-5_3.2_4.1-a $5$ 5T5 $[5, 6, 4]$ $[[5], [3, 2], [4, 1]]$ $1$ $2$ \(\Q(\sqrt{6}) \) $[[[2, 3, 4, 5, 1], [2, 3, 1, 5, 4], [4, 3, 1, 2, 5]], [[2, 3, 4, 5, 1], [3, 5, 1, 2, 4], [2, 3, 4, 1, 5]]]$ 5T5-5_3.2_4.1-a
5T5-5_4.1_4.1-a $5$ 5T5 $[5, 4, 4]$ $[[5], [4, 1], [4, 1]]$ $1$ $1$ \(\Q\) $[[[4, 5, 1, 2, 3], [2, 3, 4, 1, 5], [2, 3, 5, 4, 1]]]$ 5T5-5_4.1_4.1-a
  displayed columns for results