LMFDB - Belyi maps with group 7T6

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Degree	Group	Orders	$[a,b,c]$ triple

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Label	Degree	Group	abc	Ramification type	Genus	Orbit Size	Base field	Triples	Primitivization
7T6-3.2.2_3.2.2_3.2.2-a	$7$	7T6	$[6, 6, 6]$	$[[3, 2, 2], [3, 2, 2], [3, 2, 2]]$	$0$	$1$	$\Q$	$[[[2, 3, 1, 5, 4, 7, 6], [5, 7, 4, 3, 6, 1, 2], [4, 6, 7, 1, 3, 2, 5]]]$	7T6-3.2.2_3.2.2_3.2.2-a
7T6-3.2.2_3.2.2_3.3.1-a	$7$	7T6	$[6, 6, 3]$	$[[3, 2, 2], [3, 2, 2], [3, 3, 1]]$	$0$	$1$	$\Q$	$[[[2, 3, 1, 5, 4, 7, 6], [7, 1, 4, 3, 6, 5, 2], [4, 2, 7, 6, 3, 1, 5]]]$	7T6-3.2.2_3.2.2_3.3.1-a
7T6-3.2.2_3.3.1_3.3.1-a	$7$	7T6	$[6, 3, 3]$	$[[3, 2, 2], [3, 3, 1], [3, 3, 1]]$	$0$	$1$	$\Q$	$[[[5, 7, 1, 6, 3, 4, 2], [2, 3, 1, 5, 6, 4, 7], [2, 7, 4, 5, 3, 6, 1]]]$	7T6-3.2.2_3.3.1_3.3.1-a
7T6-4.2.1_3.2.2_3.2.2-a	$7$	7T6	$[4, 6, 6]$	$[[4, 2, 1], [3, 2, 2], [3, 2, 2]]$	$0$	$2$	$\Q(\sqrt{105}) $	$[[[6, 2, 1, 7, 3, 5, 4], [2, 3, 1, 5, 4, 7, 6], [2, 1, 4, 6, 7, 3, 5]], [[5, 6, 7, 4, 3, 2, 1], [2, 3, 1, 5, 4, 7, 6], [6, 7, 4, 5, 3, 1, 2]]]$	7T6-4.2.1_3.2.2_3.2.2-a
7T6-4.2.1_3.2.2_3.3.1-a	$7$	7T6	$[4, 6, 3]$	$[[4, 2, 1], [3, 2, 2], [3, 3, 1]]$	$0$	$3$	3.1.1512.1	$[[[2, 3, 4, 1, 6, 5, 7], [3, 7, 1, 5, 6, 4, 2], [6, 3, 7, 1, 5, 4, 2]], [[2, 3, 4, 1, 6, 5, 7], [2, 1, 6, 5, 4, 7, 3], [5, 2, 1, 7, 3, 4, 6]], [[2, 3, 4, 1, 6, 5, 7], [7, 3, 2, 5, 4, 1, 6], [5, 6, 3, 2, 7, 4, 1]]]$	7T6-4.2.1_3.2.2_3.3.1-a
7T6-4.2.1_4.2.1_3.2.2-a	$7$	7T6	$[4, 4, 6]$	$[[4, 2, 1], [4, 2, 1], [3, 2, 2]]$	$0$	$2$	$\Q(\sqrt{7}) $	$[[[2, 3, 4, 1, 6, 5, 7], [3, 5, 1, 4, 7, 2, 6], [4, 3, 6, 1, 7, 2, 5]], [[2, 3, 4, 1, 6, 5, 7], [5, 2, 7, 6, 3, 4, 1], [6, 7, 2, 5, 4, 1, 3]]]$	7T6-4.2.1_4.2.1_3.2.2-a
7T6-4.2.1_4.2.1_3.2.2-b	$7$	7T6	$[4, 4, 6]$	$[[4, 2, 1], [4, 2, 1], [3, 2, 2]]$	$0$	$4$	4.0.33600.4	$[[[2, 3, 4, 1, 6, 5, 7], [6, 2, 5, 7, 4, 1, 3], [5, 6, 2, 7, 1, 3, 4]], [[2, 3, 4, 1, 6, 5, 7], [1, 6, 5, 7, 4, 2, 3], [5, 1, 6, 7, 2, 3, 4]], [[2, 3, 4, 1, 6, 5, 7], [3, 5, 6, 4, 2, 7, 1], [4, 7, 5, 1, 3, 2, 6]], [[2, 3, 4, 1, 6, 5, 7], [3, 5, 7, 4, 2, 1, 6], [4, 6, 5, 1, 7, 2, 3]]]$	7T6-4.2.1_4.2.1_3.2.2-b
7T6-4.2.1_4.2.1_3.3.1-a	$7$	7T6	$[4, 4, 3]$	$[[4, 2, 1], [4, 2, 1], [3, 3, 1]]$	$0$	$4$	4.0.3024.1	$[[[2, 3, 4, 1, 6, 5, 7], [6, 2, 5, 3, 7, 1, 4], [7, 6, 2, 4, 1, 3, 5]], [[2, 3, 4, 1, 6, 5, 7], [6, 7, 2, 4, 3, 1, 5], [4, 6, 3, 5, 1, 7, 2]], [[2, 3, 4, 1, 6, 5, 7], [3, 1, 5, 7, 2, 6, 4], [7, 2, 5, 1, 6, 3, 4]], [[2, 3, 4, 1, 6, 5, 7], [3, 5, 2, 7, 1, 6, 4], [7, 5, 3, 1, 6, 2, 4]]]$	7T6-4.2.1_4.2.1_3.3.1-a
7T6-4.2.1_4.2.1_4.2.1-a	$7$	7T6	$[4, 4, 4]$	$[[4, 2, 1], [4, 2, 1], [4, 2, 1]]$	$0$	$12$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$[[[2, 3, 4, 1, 6, 5, 7], [2, 6, 4, 3, 5, 7, 1], [3, 7, 1, 4, 2, 5, 6]], [[2, 3, 4, 1, 6, 5, 7], [3, 1, 7, 5, 4, 6, 2], [5, 2, 7, 1, 6, 4, 3]], [[2, 3, 4, 1, 6, 5, 7], [2, 7, 4, 3, 5, 1, 6], [3, 6, 1, 4, 7, 5, 2]], [[2, 3, 4, 1, 6, 5, 7], [3, 7, 2, 5, 4, 6, 1], [5, 7, 3, 1, 6, 4, 2]], [[2, 3, 4, 1, 6, 5, 7], [5, 3, 2, 4, 7, 1, 6], [4, 6, 3, 2, 7, 1, 5]], [[2, 3, 4, 1, 6, 5, 7], [3, 5, 1, 4, 6, 7, 2], [4, 3, 7, 1, 5, 2, 6]], [[2, 3, 4, 1, 6, 5, 7], [7, 2, 4, 5, 6, 3, 1], [3, 7, 2, 6, 5, 4, 1]], [[2, 3, 4, 1, 6, 5, 7], [3, 7, 1, 4, 6, 2, 5], [4, 3, 6, 1, 5, 7, 2]], [[2, 3, 4, 1, 6, 5, 7], [7, 3, 5, 4, 6, 2, 1], [4, 7, 6, 2, 5, 3, 1]], [[2, 3, 4, 1, 6, 5, 7], [1, 4, 2, 5, 3, 7, 6], [2, 1, 3, 5, 7, 4, 6]], [[2, 3, 4, 1, 6, 5, 7], [1, 4, 5, 3, 2, 7, 6], [2, 1, 5, 4, 7, 3, 6]], [[2, 3, 4, 1, 6, 5, 7], [2, 1, 5, 4, 7, 3, 6], [4, 2, 1, 6, 7, 3, 5]]]$	7T6-4.2.1_4.2.1_4.2.1-a
7T6-5.1.1_3.2.2_3.2.2-a	$7$	7T6	$[5, 6, 6]$	$[[5, 1, 1], [3, 2, 2], [3, 2, 2]]$	$0$	$1$	$\Q$	$[[[4, 2, 1, 7, 3, 6, 5], [2, 3, 1, 5, 4, 7, 6], [2, 1, 4, 3, 6, 7, 5]]]$	7T6-5.1.1_3.2.2_3.2.2-a
7T6-5.1.1_3.2.2_3.3.1-a	$7$	7T6	$[5, 6, 3]$	$[[5, 1, 1], [3, 2, 2], [3, 3, 1]]$	$0$	$3$	3.3.2700.1	$[[[2, 3, 4, 5, 1, 6, 7], [4, 7, 1, 3, 6, 5, 2], [6, 3, 7, 4, 1, 5, 2]], [[2, 3, 4, 5, 1, 6, 7], [7, 5, 4, 3, 6, 2, 1], [2, 7, 6, 4, 3, 5, 1]], [[2, 3, 4, 5, 1, 6, 7], [3, 7, 1, 6, 4, 5, 2], [6, 3, 7, 1, 5, 4, 2]]]$	7T6-5.1.1_3.2.2_3.3.1-a
7T6-5.1.1_3.2.2_5.1.1-a	$7$	7T6	$[5, 6, 5]$	$[[5, 1, 1], [3, 2, 2], [5, 1, 1]]$	$0$	$2$	$\Q(\sqrt{3}) $	$[[[2, 3, 4, 5, 1, 6, 7], [7, 4, 2, 3, 6, 5, 1], [6, 7, 3, 4, 2, 5, 1]], [[2, 3, 4, 5, 1, 6, 7], [2, 1, 4, 3, 6, 7, 5], [7, 2, 1, 4, 3, 5, 6]]]$	7T6-5.1.1_3.2.2_5.1.1-a
7T6-5.1.1_3.2.2_5.1.1-b	$7$	7T6	$[5, 6, 5]$	$[[5, 1, 1], [3, 2, 2], [5, 1, 1]]$	$0$	$2$	$\Q(\sqrt{-5}) $	$[[[2, 3, 4, 5, 1, 6, 7], [7, 3, 2, 6, 4, 5, 1], [6, 7, 3, 2, 5, 4, 1]], [[2, 3, 4, 5, 1, 6, 7], [5, 3, 2, 6, 7, 4, 1], [1, 7, 3, 2, 6, 4, 5]]]$	7T6-5.1.1_3.2.2_5.1.1-b
7T6-5.1.1_3.3.1_3.3.1-a	$7$	7T6	$[5, 3, 3]$	$[[5, 1, 1], [3, 3, 1], [3, 3, 1]]$	$0$	$1$	$\Q$	$[[[7, 5, 3, 1, 4, 6, 2], [2, 3, 1, 5, 6, 4, 7], [6, 7, 2, 4, 1, 5, 3]]]$	7T6-5.1.1_3.3.1_3.3.1-a
7T6-5.1.1_3.3.1_4.2.1-a	$7$	7T6	$[5, 3, 4]$	$[[5, 1, 1], [3, 3, 1], [4, 2, 1]]$	$0$	$5$	5.1.1512000.1	$[[[2, 5, 3, 4, 6, 7, 1], [4, 7, 1, 3, 5, 2, 6], [2, 3, 4, 1, 6, 5, 7]], [[2, 7, 3, 4, 6, 1, 5], [4, 6, 1, 3, 5, 7, 2], [2, 3, 4, 1, 6, 5, 7]], [[7, 2, 3, 5, 6, 1, 4], [3, 6, 7, 2, 5, 4, 1], [2, 4, 1, 3, 6, 5, 7]], [[7, 1, 3, 5, 2, 6, 4], [3, 2, 7, 5, 6, 4, 1], [2, 4, 1, 3, 6, 5, 7]], [[7, 5, 3, 2, 1, 6, 4], [3, 5, 7, 4, 6, 2, 1], [2, 4, 1, 3, 6, 5, 7]]]$	7T6-5.1.1_3.3.1_4.2.1-a
7T6-5.1.1_4.2.1_3.2.2-a	$7$	7T6	$[5, 4, 6]$	$[[5, 1, 1], [4, 2, 1], [3, 2, 2]]$	$0$	$1$	$\Q$	$[[[5, 2, 1, 4, 7, 3, 6], [2, 3, 4, 1, 6, 5, 7], [2, 1, 5, 3, 4, 7, 6]]]$	7T6-5.1.1_4.2.1_3.2.2-a
7T6-5.1.1_4.2.1_3.2.2-b	$7$	7T6	$[5, 4, 6]$	$[[5, 1, 1], [4, 2, 1], [3, 2, 2]]$	$0$	$3$	3.1.4200.1	$[[[5, 2, 3, 1, 7, 4, 6], [2, 3, 4, 1, 6, 5, 7], [3, 1, 2, 5, 4, 7, 6]], [[6, 7, 3, 2, 5, 4, 1], [2, 3, 4, 1, 6, 5, 7], [7, 3, 2, 5, 6, 4, 1]], [[4, 7, 3, 6, 5, 2, 1], [2, 4, 1, 3, 6, 5, 7], [7, 5, 4, 3, 6, 2, 1]]]$	7T6-5.1.1_4.2.1_3.2.2-b
7T6-5.1.1_4.2.1_4.2.1-a	$7$	7T6	$[5, 4, 4]$	$[[5, 1, 1], [4, 2, 1], [4, 2, 1]]$	$0$	$3$	3.1.140.1	$[[[4, 7, 3, 2, 5, 1, 6], [2, 3, 4, 1, 6, 5, 7], [5, 3, 2, 4, 6, 7, 1]], [[7, 2, 3, 5, 6, 1, 4], [2, 3, 4, 1, 6, 5, 7], [5, 1, 2, 7, 3, 6, 4]], [[4, 2, 1, 6, 5, 7, 3], [2, 3, 4, 1, 6, 5, 7], [2, 1, 7, 4, 6, 3, 5]]]$	7T6-5.1.1_4.2.1_4.2.1-a
7T6-5.1.1_4.2.1_4.2.1-b	$7$	7T6	$[5, 4, 4]$	$[[5, 1, 1], [4, 2, 1], [4, 2, 1]]$	$0$	$8$	8.2.$\cdots$.4	$[[[3, 2, 7, 4, 1, 5, 6], [2, 3, 4, 1, 6, 5, 7], [6, 1, 4, 3, 5, 7, 2]], [[6, 2, 1, 3, 5, 7, 4], [2, 3, 4, 1, 6, 5, 7], [2, 1, 3, 7, 6, 4, 5]], [[3, 2, 6, 4, 7, 5, 1], [2, 3, 4, 1, 6, 5, 7], [7, 1, 4, 3, 5, 2, 6]], [[6, 7, 2, 4, 5, 3, 1], [2, 3, 4, 1, 6, 5, 7], [7, 2, 5, 3, 6, 4, 1]], [[4, 7, 3, 6, 5, 2, 1], [2, 3, 4, 1, 6, 5, 7], [7, 5, 2, 4, 6, 3, 1]], [[5, 1, 3, 4, 7, 2, 6], [2, 3, 4, 1, 6, 5, 7], [1, 5, 2, 3, 4, 7, 6]], [[5, 2, 3, 7, 6, 4, 1], [2, 3, 4, 1, 6, 5, 7], [7, 1, 2, 5, 4, 6, 3]], [[3, 7, 2, 4, 5, 1, 6], [2, 3, 4, 1, 6, 5, 7], [5, 2, 4, 3, 6, 7, 1]]]$	7T6-5.1.1_4.2.1_4.2.1-b
7T6-5.1.1_5.1.1_3.3.1-a	$7$	7T6	$[5, 5, 3]$	$[[5, 1, 1], [5, 1, 1], [3, 3, 1]]$	$0$	$3$	3.1.135.1	$[[[2, 3, 4, 5, 1, 6, 7], [3, 1, 6, 4, 5, 7, 2], [5, 2, 7, 1, 4, 3, 6]], [[2, 3, 4, 5, 1, 6, 7], [3, 6, 2, 4, 5, 7, 1], [5, 7, 3, 1, 4, 2, 6]], [[2, 3, 4, 5, 1, 6, 7], [1, 7, 3, 6, 4, 2, 5], [7, 1, 6, 3, 5, 4, 2]]]$	7T6-5.1.1_5.1.1_3.3.1-a
7T6-5.1.1_5.1.1_4.2.1-a	$7$	7T6	$[5, 5, 4]$	$[[5, 1, 1], [5, 1, 1], [4, 2, 1]]$	$0$	$4$	4.0.60480.4	$[[[4, 2, 3, 5, 6, 7, 1], [1, 7, 2, 3, 5, 4, 6], [2, 3, 4, 1, 6, 5, 7]], [[4, 2, 3, 7, 6, 1, 5], [1, 6, 2, 3, 5, 7, 4], [2, 3, 4, 1, 6, 5, 7]], [[4, 2, 5, 3, 7, 6, 1], [1, 7, 2, 4, 6, 3, 5], [2, 3, 4, 1, 6, 5, 7]], [[7, 1, 3, 2, 4, 6, 5], [3, 2, 5, 4, 6, 7, 1], [2, 4, 1, 3, 6, 5, 7]]]$	7T6-5.1.1_5.1.1_4.2.1-a
7T6-5.1.1_5.1.1_5.1.1-a	$7$	7T6	$[5, 5, 5]$	$[[5, 1, 1], [5, 1, 1], [5, 1, 1]]$	$0$	$1$	$\Q$	$[[[2, 3, 4, 5, 1, 6, 7], [5, 1, 3, 4, 6, 7, 2], [1, 2, 7, 3, 4, 5, 6]]]$	7T6-5.1.1_5.1.1_5.1.1-a
7T6-7_2.2.1.1.1_3.2.2-a	$7$	7T6	$[7, 2, 6]$	$[[7], [2, 2, 1, 1, 1], [3, 2, 2]]$	$0$	$2$	$\Q(\sqrt{21}) $	$[[[3, 7, 5, 2, 4, 1, 6], [2, 1, 4, 3, 5, 6, 7], [6, 3, 2, 5, 4, 7, 1]], [[5, 7, 6, 2, 3, 4, 1], [2, 1, 4, 3, 5, 6, 7], [7, 3, 5, 6, 2, 4, 1]]]$	7T6-7_2.2.1.1.1_3.2.2-a
7T6-7_2.2.1.1.1_4.2.1-a	$7$	7T6	$[7, 2, 4]$	$[[7], [2, 2, 1, 1, 1], [4, 2, 1]]$	$0$	$2$	$\Q(\sqrt{21}) $	$[[[3, 7, 4, 2, 1, 5, 6], [2, 1, 4, 3, 5, 6, 7], [5, 3, 2, 4, 6, 7, 1]], [[7, 6, 5, 3, 1, 4, 2], [2, 1, 4, 3, 5, 6, 7], [5, 7, 3, 6, 4, 1, 2]]]$	7T6-7_2.2.1.1.1_4.2.1-a
7T6-7_2.2.1.1.1_5.1.1-a	$7$	7T6	$[7, 2, 5]$	$[[7], [2, 2, 1, 1, 1], [5, 1, 1]]$	$0$	$2$	$\Q(\sqrt{21}) $	$[[[2, 7, 1, 3, 4, 5, 6], [2, 1, 4, 3, 5, 6, 7], [4, 2, 3, 5, 6, 7, 1]], [[2, 7, 5, 3, 1, 4, 6], [2, 1, 4, 3, 5, 6, 7], [5, 2, 3, 6, 4, 7, 1]]]$	7T6-7_2.2.1.1.1_5.1.1-a
7T6-7_3.1.1.1.1_3.2.2-a	$7$	7T6	$[7, 3, 6]$	$[[7], [3, 1, 1, 1, 1], [3, 2, 2]]$	$0$	$1$	$\Q$	$[[[3, 1, 4, 5, 6, 7, 2], [1, 2, 7, 4, 3, 6, 5], [2, 3, 1, 5, 4, 7, 6]]]$	7T6-7_3.1.1.1.1_3.2.2-a
7T6-7_3.1.1.1.1_3.3.1-a	$7$	7T6	$[7, 3, 3]$	$[[7], [3, 1, 1, 1, 1], [3, 3, 1]]$	$0$	$1$	$\Q$	$[[[3, 1, 4, 6, 7, 5, 2], [1, 2, 7, 4, 3, 6, 5], [2, 3, 1, 5, 6, 4, 7]]]$	7T6-7_3.1.1.1.1_3.3.1-a
7T6-7_3.1.1.1.1_4.2.1-a	$7$	7T6	$[7, 3, 4]$	$[[7], [3, 1, 1, 1, 1], [4, 2, 1]]$	$0$	$2$	$\Q(\sqrt{-14}) $	$[[[4, 5, 2, 3, 6, 7, 1], [1, 7, 3, 4, 5, 2, 6], [2, 3, 4, 1, 6, 5, 7]], [[4, 7, 2, 3, 6, 1, 5], [1, 6, 3, 4, 5, 7, 2], [2, 3, 4, 1, 6, 5, 7]]]$	7T6-7_3.1.1.1.1_4.2.1-a
7T6-7_3.1.1.1.1_5.1.1-a	$7$	7T6	$[7, 3, 5]$	$[[7], [3, 1, 1, 1, 1], [5, 1, 1]]$	$0$	$1$	$\Q$	$[[[5, 1, 2, 6, 4, 7, 3], [1, 2, 3, 7, 5, 4, 6], [2, 3, 4, 5, 1, 6, 7]]]$	7T6-7_3.1.1.1.1_5.1.1-a
7T6-7_3.2.2_3.2.2-a	$7$	7T6	$[7, 6, 6]$	$[[7], [3, 2, 2], [3, 2, 2]]$	$1$	$2$	$\Q(\sqrt{21}) $	$[[[4, 7, 1, 6, 3, 2, 5], [2, 3, 1, 5, 4, 7, 6], [2, 7, 4, 3, 6, 5, 1]], [[4, 5, 7, 6, 3, 2, 1], [2, 3, 1, 5, 4, 7, 6], [6, 7, 4, 3, 1, 5, 2]]]$	7T6-7_3.2.2_3.2.2-a
7T6-7_3.2.2_3.3.1-a	$7$	7T6	$[7, 6, 3]$	$[[7], [3, 2, 2], [3, 3, 1]]$	$1$	$3$	3.1.3780.1	$[[[2, 5, 4, 7, 3, 1, 6], [5, 6, 1, 7, 3, 2, 4], [2, 3, 1, 5, 6, 4, 7]], [[6, 4, 5, 3, 1, 7, 2], [4, 5, 7, 1, 2, 3, 6], [2, 3, 1, 5, 6, 4, 7]], [[7, 5, 4, 2, 6, 1, 3], [7, 6, 4, 5, 3, 2, 1], [2, 3, 1, 5, 6, 4, 7]]]$	7T6-7_3.2.2_3.3.1-a
7T6-7_4.2.1_3.2.2-a	$7$	7T6	$[7, 4, 6]$	$[[7], [4, 2, 1], [3, 2, 2]]$	$1$	$2$	$\Q(\sqrt{70}) $	$[[[2, 3, 6, 5, 7, 4, 1], [2, 7, 1, 4, 6, 5, 3], [2, 3, 1, 5, 4, 7, 6]], [[7, 5, 2, 3, 6, 1, 4], [4, 6, 3, 2, 7, 1, 5], [2, 3, 1, 5, 4, 7, 6]]]$	7T6-7_4.2.1_3.2.2-a
7T6-7_4.2.1_3.2.2-b	$7$	7T6	$[7, 4, 6]$	$[[7], [4, 2, 1], [3, 2, 2]]$	$1$	$6$	6.2.62233920.1	$[[[3, 7, 4, 6, 2, 5, 1], [1, 7, 5, 6, 3, 2, 4], [2, 3, 1, 5, 4, 7, 6]], [[7, 3, 6, 5, 1, 4, 2], [2, 5, 7, 4, 6, 1, 3], [2, 3, 1, 5, 4, 7, 6]], [[2, 7, 4, 5, 6, 1, 3], [7, 6, 1, 4, 3, 2, 5], [2, 3, 1, 5, 4, 7, 6]], [[6, 4, 5, 3, 1, 7, 2], [4, 5, 7, 3, 2, 6, 1], [2, 3, 1, 5, 4, 7, 6]], [[3, 6, 4, 2, 7, 5, 1], [1, 7, 4, 6, 3, 5, 2], [2, 3, 1, 5, 4, 7, 6]], [[6, 7, 4, 5, 2, 3, 1], [6, 7, 5, 4, 3, 2, 1], [2, 3, 1, 5, 4, 7, 6]]]$	7T6-7_4.2.1_3.2.2-b
7T6-7_4.2.1_3.3.1-a	$7$	7T6	$[7, 4, 3]$	$[[7], [4, 2, 1], [3, 3, 1]]$	$1$	$6$	6.0.165957120.2	$[[[3, 7, 4, 5, 6, 2, 1], [1, 7, 6, 5, 3, 4, 2], [2, 3, 1, 5, 6, 4, 7]], [[2, 3, 5, 7, 4, 1, 6], [2, 6, 1, 7, 5, 3, 4], [2, 3, 1, 5, 6, 4, 7]], [[7, 5, 4, 6, 3, 1, 2], [5, 6, 7, 4, 3, 2, 1], [2, 3, 1, 5, 6, 4, 7]], [[4, 1, 5, 3, 7, 2, 6], [4, 2, 6, 7, 1, 3, 5], [2, 3, 1, 5, 6, 4, 7]], [[7, 3, 4, 6, 2, 1, 5], [2, 6, 5, 4, 3, 7, 1], [2, 3, 1, 5, 6, 4, 7]], [[3, 7, 4, 5, 2, 1, 6], [1, 6, 5, 7, 3, 4, 2], [2, 3, 1, 5, 6, 4, 7]]]$	7T6-7_4.2.1_3.3.1-a
7T6-7_4.2.1_4.2.1-a	$7$	7T6	$[7, 4, 4]$	$[[7], [4, 2, 1], [4, 2, 1]]$	$1$	$2$	$\Q(\sqrt{21}) $	$[[[7, 5, 1, 2, 6, 3, 4], [2, 3, 4, 1, 6, 5, 7], [2, 3, 5, 7, 1, 6, 4]], [[6, 5, 2, 7, 4, 3, 1], [2, 3, 4, 1, 6, 5, 7], [7, 2, 5, 6, 1, 4, 3]]]$	7T6-7_4.2.1_4.2.1-a
7T6-7_4.2.1_4.2.1-b	$7$	7T6	$[7, 4, 4]$	$[[7], [4, 2, 1], [4, 2, 1]]$	$1$	$8$	8.2.$\cdots$.2	$[[[5, 7, 1, 2, 6, 4, 3], [2, 3, 4, 1, 6, 5, 7], [2, 3, 7, 5, 4, 6, 1]], [[3, 1, 5, 2, 7, 4, 6], [2, 3, 4, 1, 6, 5, 7], [1, 3, 4, 5, 2, 7, 6]], [[7, 6, 2, 5, 1, 4, 3], [2, 3, 4, 1, 6, 5, 7], [6, 2, 7, 5, 3, 1, 4]], [[7, 1, 6, 5, 2, 4, 3], [2, 3, 4, 1, 6, 5, 7], [1, 6, 7, 5, 3, 2, 4]], [[7, 3, 1, 5, 6, 2, 4], [2, 3, 4, 1, 6, 5, 7], [2, 5, 1, 7, 3, 6, 4]], [[6, 7, 2, 1, 4, 3, 5], [2, 3, 4, 1, 6, 5, 7], [3, 2, 5, 6, 7, 4, 1]], [[7, 3, 6, 2, 1, 5, 4], [2, 3, 4, 1, 6, 5, 7], [6, 3, 1, 7, 5, 2, 4]], [[4, 3, 5, 6, 7, 2, 1], [2, 3, 4, 1, 6, 5, 7], [7, 5, 1, 4, 2, 3, 6]]]$	7T6-7_4.2.1_4.2.1-b
7T6-7_4.2.1_4.2.1-c	$7$	7T6	$[7, 4, 4]$	$[[7], [4, 2, 1], [4, 2, 1]]$	$1$	$12$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$[[[5, 3, 7, 2, 6, 4, 1], [2, 3, 4, 1, 6, 5, 7], [7, 3, 1, 5, 4, 6, 2]], [[5, 7, 2, 6, 4, 3, 1], [2, 3, 4, 1, 6, 5, 7], [7, 2, 5, 6, 4, 3, 1]], [[5, 1, 4, 2, 7, 3, 6], [2, 3, 4, 1, 6, 5, 7], [1, 3, 5, 2, 4, 7, 6]], [[3, 6, 2, 5, 1, 7, 4], [2, 3, 4, 1, 6, 5, 7], [6, 2, 4, 7, 3, 1, 5]], [[5, 1, 7, 6, 4, 3, 2], [2, 3, 4, 1, 6, 5, 7], [1, 7, 5, 6, 4, 3, 2]], [[3, 1, 6, 7, 2, 4, 5], [2, 3, 4, 1, 6, 5, 7], [1, 6, 4, 5, 7, 2, 3]], [[5, 7, 6, 3, 4, 2, 1], [2, 3, 4, 1, 6, 5, 7], [7, 5, 3, 6, 4, 2, 1]], [[3, 1, 4, 5, 7, 2, 6], [2, 3, 4, 1, 6, 5, 7], [1, 5, 4, 2, 3, 7, 6]], [[2, 7, 4, 1, 3, 5, 6], [2, 3, 4, 1, 6, 5, 7], [3, 4, 6, 2, 5, 7, 1]], [[5, 3, 1, 7, 6, 4, 2], [2, 3, 4, 1, 6, 5, 7], [2, 7, 1, 5, 4, 6, 3]], [[2, 6, 4, 1, 7, 5, 3], [2, 3, 4, 1, 6, 5, 7], [3, 4, 7, 2, 5, 1, 6]], [[2, 6, 4, 7, 3, 5, 1], [2, 3, 4, 1, 6, 5, 7], [7, 4, 6, 2, 5, 1, 3]]]$	7T6-7_4.2.1_4.2.1-c
7T6-7_4.2.1_5.1.1-a	$7$	7T6	$[7, 4, 5]$	$[[7], [4, 2, 1], [5, 1, 1]]$	$1$	$6$	6.0.460992000.1	$[[[3, 7, 5, 6, 4, 2, 1], [3, 7, 6, 1, 5, 4, 2], [2, 3, 4, 5, 1, 6, 7]], [[2, 7, 1, 3, 6, 4, 5], [7, 3, 1, 4, 6, 5, 2], [2, 3, 4, 5, 1, 6, 7]], [[2, 5, 7, 6, 4, 3, 1], [2, 7, 1, 6, 5, 4, 3], [2, 3, 4, 5, 1, 6, 7]], [[7, 4, 2, 1, 6, 3, 5], [7, 4, 3, 6, 2, 5, 1], [2, 3, 4, 5, 1, 6, 7]], [[5, 7, 1, 2, 6, 4, 3], [1, 3, 4, 7, 6, 5, 2], [2, 3, 4, 5, 1, 6, 7]], [[4, 5, 2, 6, 7, 3, 1], [2, 7, 3, 6, 1, 4, 5], [2, 3, 4, 5, 1, 6, 7]]]$	7T6-7_4.2.1_5.1.1-a
7T6-7_4.2.1_5.1.1-b	$7$	7T6	$[7, 4, 5]$	$[[7], [4, 2, 1], [5, 1, 1]]$	$1$	$12$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$[[[3, 1, 4, 5, 6, 7, 2], [4, 2, 7, 1, 3, 5, 6], [2, 3, 4, 5, 1, 6, 7]], [[2, 3, 5, 6, 4, 7, 1], [3, 7, 1, 2, 5, 4, 6], [2, 3, 4, 5, 1, 6, 7]], [[2, 4, 5, 3, 6, 7, 1], [3, 7, 1, 4, 2, 5, 6], [2, 3, 4, 5, 1, 6, 7]], [[3, 4, 2, 5, 6, 7, 1], [4, 7, 3, 1, 2, 5, 6], [2, 3, 4, 5, 1, 6, 7]], [[7, 4, 2, 6, 1, 5, 3], [6, 5, 3, 7, 2, 4, 1], [2, 3, 4, 5, 1, 6, 7]], [[3, 6, 2, 5, 7, 4, 1], [4, 7, 3, 1, 6, 2, 5], [2, 3, 4, 5, 1, 6, 7]], [[4, 7, 5, 3, 6, 2, 1], [3, 7, 6, 4, 1, 5, 2], [2, 3, 4, 5, 1, 6, 7]], [[3, 5, 6, 7, 4, 2, 1], [2, 7, 6, 1, 5, 3, 4], [2, 3, 4, 5, 1, 6, 7]], [[4, 6, 2, 5, 7, 1, 3], [4, 6, 3, 7, 1, 2, 5], [2, 3, 4, 5, 1, 6, 7]], [[3, 5, 2, 6, 7, 1, 4], [2, 6, 3, 1, 7, 4, 5], [2, 3, 4, 5, 1, 6, 7]], [[7, 5, 2, 1, 6, 4, 3], [2, 4, 3, 7, 6, 5, 1], [2, 3, 4, 5, 1, 6, 7]], [[7, 3, 1, 6, 4, 2, 5], [7, 3, 6, 2, 5, 4, 1], [2, 3, 4, 5, 1, 6, 7]]]$	7T6-7_4.2.1_5.1.1-b
7T6-7_5.1.1_3.2.2-a	$7$	7T6	$[7, 5, 6]$	$[[7], [5, 1, 1], [3, 2, 2]]$	$1$	$1$	$\Q$	$[[[6, 3, 4, 5, 1, 7, 2], [2, 5, 7, 4, 3, 6, 1], [2, 3, 1, 5, 4, 7, 6]]]$	7T6-7_5.1.1_3.2.2-a
7T6-7_5.1.1_3.2.2-b	$7$	7T6	$[7, 5, 6]$	$[[7], [5, 1, 1], [3, 2, 2]]$	$1$	$6$	6.2.388962000.3	$[[[2, 3, 4, 5, 6, 7, 1], [2, 7, 1, 4, 3, 6, 5], [2, 3, 1, 5, 4, 7, 6]], [[3, 7, 4, 5, 6, 2, 1], [1, 7, 6, 4, 3, 2, 5], [2, 3, 1, 5, 4, 7, 6]], [[3, 1, 4, 6, 7, 5, 2], [1, 2, 7, 6, 3, 5, 4], [2, 3, 1, 5, 4, 7, 6]], [[4, 1, 5, 3, 6, 7, 2], [4, 2, 7, 3, 1, 6, 5], [2, 3, 1, 5, 4, 7, 6]], [[7, 1, 6, 3, 4, 2, 5], [4, 2, 6, 7, 5, 1, 3], [2, 3, 1, 5, 4, 7, 6]], [[7, 1, 4, 5, 6, 2, 3], [7, 2, 6, 4, 3, 1, 5], [2, 3, 1, 5, 4, 7, 6]]]$	7T6-7_5.1.1_3.2.2-b
7T6-7_5.1.1_3.3.1-a	$7$	7T6	$[7, 5, 3]$	$[[7], [5, 1, 1], [3, 3, 1]]$	$1$	$3$	3.1.175.1	$[[[3, 1, 4, 5, 6, 7, 2], [1, 2, 7, 5, 3, 4, 6], [2, 3, 1, 5, 6, 4, 7]], [[2, 3, 4, 6, 7, 5, 1], [2, 7, 1, 4, 3, 6, 5], [2, 3, 1, 5, 6, 4, 7]], [[5, 1, 4, 6, 3, 7, 2], [5, 2, 7, 4, 3, 1, 6], [2, 3, 1, 5, 6, 4, 7]]]$	7T6-7_5.1.1_3.3.1-a
7T6-7_5.1.1_3.3.1-b	$7$	7T6	$[7, 5, 3]$	$[[7], [5, 1, 1], [3, 3, 1]]$	$1$	$5$	5.1.4630500.1	$[[[3, 1, 4, 5, 7, 2, 6], [1, 2, 6, 7, 3, 4, 5], [2, 3, 1, 5, 6, 4, 7]], [[7, 3, 4, 6, 1, 5, 2], [2, 5, 7, 4, 3, 6, 1], [2, 3, 1, 5, 6, 4, 7]], [[3, 6, 5, 2, 4, 7, 1], [1, 7, 4, 2, 5, 3, 6], [2, 3, 1, 5, 6, 4, 7]], [[3, 5, 4, 6, 1, 7, 2], [1, 5, 7, 4, 3, 2, 6], [2, 3, 1, 5, 6, 4, 7]], [[7, 4, 2, 6, 3, 1, 5], [5, 6, 3, 4, 2, 7, 1], [2, 3, 1, 5, 6, 4, 7]]]$	7T6-7_5.1.1_3.3.1-b
7T6-7_5.1.1_5.1.1-a	$7$	7T6	$[7, 5, 5]$	$[[7], [5, 1, 1], [5, 1, 1]]$	$1$	$2$	$\Q(\sqrt{-3}) $	$[[[4, 1, 2, 5, 6, 7, 3], [4, 2, 3, 7, 1, 5, 6], [2, 3, 4, 5, 1, 6, 7]], [[2, 5, 6, 3, 4, 7, 1], [2, 7, 1, 4, 5, 3, 6], [2, 3, 4, 5, 1, 6, 7]]]$	7T6-7_5.1.1_5.1.1-a
7T6-7_5.1.1_5.1.1-b	$7$	7T6	$[7, 5, 5]$	$[[7], [5, 1, 1], [5, 1, 1]]$	$1$	$2$	$\Q(\sqrt{21}) $	$[[[7, 5, 2, 6, 4, 1, 3], [2, 6, 3, 7, 5, 4, 1], [2, 3, 4, 5, 1, 6, 7]], [[4, 5, 2, 3, 6, 7, 1], [2, 7, 3, 4, 1, 5, 6], [2, 3, 4, 5, 1, 6, 7]]]$	7T6-7_5.1.1_5.1.1-b
7T6-7_5.1.1_5.1.1-c	$7$	7T6	$[7, 5, 5]$	$[[7], [5, 1, 1], [5, 1, 1]]$	$1$	$8$	8.2.$\cdots$.1	$[[[3, 1, 5, 6, 4, 7, 2], [3, 2, 7, 1, 5, 4, 6], [2, 3, 4, 5, 1, 6, 7]], [[4, 1, 5, 3, 6, 7, 2], [3, 2, 7, 4, 1, 5, 6], [2, 3, 4, 5, 1, 6, 7]], [[3, 5, 2, 6, 4, 7, 1], [2, 7, 3, 1, 5, 4, 6], [2, 3, 4, 5, 1, 6, 7]], [[4, 6, 2, 3, 7, 5, 1], [6, 7, 3, 4, 1, 2, 5], [2, 3, 4, 5, 1, 6, 7]], [[7, 5, 2, 3, 6, 1, 4], [2, 6, 3, 4, 7, 5, 1], [2, 3, 4, 5, 1, 6, 7]], [[5, 4, 2, 7, 6, 3, 1], [1, 7, 3, 6, 2, 5, 4], [2, 3, 4, 5, 1, 6, 7]], [[5, 4, 7, 3, 6, 2, 1], [1, 7, 6, 4, 2, 5, 3], [2, 3, 4, 5, 1, 6, 7]], [[5, 1, 4, 6, 7, 2, 3], [1, 2, 6, 7, 3, 4, 5], [2, 3, 4, 5, 1, 6, 7]]]$	7T6-7_5.1.1_5.1.1-c
7T6-7_7_2.2.1.1.1-a	$7$	7T6	$[7, 7, 2]$	$[[7], [7], [2, 2, 1, 1, 1]]$	$1$	$1$	$\Q$	$[[[7, 5, 2, 6, 4, 1, 3], [3, 6, 5, 7, 2, 4, 1], [2, 1, 4, 3, 5, 6, 7]]]$	7T6-7_7_2.2.1.1.1-a
7T6-7_7_2.2.1.1.1-b	$7$	7T6	$[7, 7, 2]$	$[[7], [7], [2, 2, 1, 1, 1]]$	$1$	$2$	$\Q(\sqrt{21}) $	$[[[3, 4, 2, 5, 6, 7, 1], [3, 7, 2, 1, 4, 5, 6], [2, 1, 4, 3, 5, 6, 7]], [[3, 4, 7, 5, 6, 1, 2], [7, 6, 2, 1, 4, 5, 3], [2, 1, 4, 3, 5, 6, 7]]]$	7T6-7_7_2.2.1.1.1-b
7T6-7_7_3.1.1.1.1-a	$7$	7T6	$[7, 7, 3]$	$[[7], [7], [3, 1, 1, 1, 1]]$	$1$	$2$	$\Q(\sqrt{21}) $	$[[[2, 3, 4, 5, 6, 7, 1], [2, 7, 1, 3, 4, 5, 6], [2, 3, 1, 4, 5, 6, 7]], [[6, 3, 4, 5, 1, 7, 2], [2, 5, 7, 3, 4, 1, 6], [2, 3, 1, 4, 5, 6, 7]]]$	7T6-7_7_3.1.1.1.1-a
7T6-7_7_3.1.1.1.1-b	$7$	7T6	$[7, 7, 3]$	$[[7], [7], [3, 1, 1, 1, 1]]$	$1$	$3$	3.1.588.1	$[[[7, 3, 4, 5, 6, 1, 2], [2, 6, 7, 3, 4, 5, 1], [2, 3, 1, 4, 5, 6, 7]], [[2, 4, 5, 3, 6, 7, 1], [4, 7, 1, 2, 3, 5, 6], [2, 3, 1, 4, 5, 6, 7]], [[7, 4, 5, 3, 6, 1, 2], [4, 6, 7, 2, 3, 5, 1], [2, 3, 1, 4, 5, 6, 7]]]$	7T6-7_7_3.1.1.1.1-b

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