trans22a.grp

#############################################################################
##
#A  trans22a.grp                 GAP group library           Alexander Hulpke
##
##
#Y  Copyright (C) 2001, Alexander Hulpke, Colorado State University
##
##  This file contains part of the transitive groups of degree 22
##

TRANSGRP[22]{[1..59]}:=
[[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22),"t22n1"],
[(1,4,6,8,10,12,14,16,18,20,21)(2,3,5,7,9,11,13,15,17,19,22),
(1,19)(2,20)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)(21,22),"t22n2"],
[(1,21)(2,22)(3,19)(4,20)(5,18)(6,17)(7,15)(8,16)(9,14)(10,13)(11,12),
(1,19)(2,20)(3,17)(4,18)(5,15)(6,16)(7,14)(8,13)(9,11)(10,12),"t22n3"],
[(1,3,8,16,10,19,17,14,5,11)(2,4,7,15,9,20,18,13,6,12)(21,22),
(1,4,5,8,10,12,13,15,17,20,21)(2,3,6,7,9,11,14,16,18,19,22),"t22n4"],
[(1,16,7,22,13,5,19,12,3,18,10,2,15,8,21,14,6,20,11,4,17,9),
(1,11,17,3,21)(2,12,18,4,22)(5,9,8,20,14)(6,10,7,19,13),"t22n5"],
[(1,2)(3,12,7,9,19,4,11,8,10,20)(5,21,14,17,16,6,22,13,18,15),
(1,19,17,6,21,7,11,13,3,10)(2,20,18,5,22,8,12,14,4,9),"t22n6"],
[(1,14)(2,21)(3,17)(4,13)(5,20)(6,16)(7,12)(8,19)(9,15)(10,22)(11,18),
(1,14,6,16,11,18,5,20,10,22,4,13,9,15,3,17,8,19,2,21,7,12),"t22n7"],
[(1,21,11,15)(2,16,10,20)(3,22,9,14)(4,17,8,19)(5,12,7,13)(6,18),
(1,8)(2,7)(3,6)(4,5)(9,11)(12,19)(13,18)(14,17)(15,16)(20,22),"t22n8"],
[(1,13,2,18,3,12,4,17,5,22,6,16,7,21,8,15,9,20,10,14,11,19),
(1,5)(2,4)(6,11)(7,10)(8,9)(13,22)(14,21)(15,20)(16,19)(17,18),"t22n9"],
[(1,15,2,20)(3,14,11,21)(4,19,10,16)(5,13,9,22)(6,18,8,17)(7,12),
(1,15)(2,21)(3,16)(4,22)(5,17)(6,12)(7,18)(8,13)(9,19)(10,14)(11,20),"t22n10"]
,[(1,18,8,12,5,13,11,22,10,15)(2,14,6,20,9,19,3,21,4,17)(7,16),
(1,18,10,14,11,16,5,15,8,21)(2,20,4,13,3,22,9,12,6,17)(7,19),"t22n11"],
[(1,22,6,16,11,21,5,15,10,20,4,14,9,19,3,13,8,18,2,12,7,17),
(1,2,5,3,8)(4,11,10,7,9)(12,14,22,21,17)(13,18,16,19,20),"t22n12"],
[(1,20,12,5,22,2,19,11,6,21)(3,17,13,8,16,4,18,14,7,15)(9,10),
(1,21,15,3,8,10)(2,22,16,4,7,9)(5,14,11,6,13,12)(17,20)(18,19),"t22n13"],
[(1,3,9)(2,4,10,11,7,5)(6,8)(12,14,15,19,13,20)(16,17,21)(18,22),
(1,14,8,18,2,16,5,21,3,15)(4,19,6,17,9,22,7,12,11,13)(10,20),"t22n14"],
[(1,22,8,19,5,14,11,13,10,15)(2,20,6,12,9,17,3,18,4,16)(7,21),
(1,10,9,3,11,4,6,7,2,5)(12,19,17,16,21,18,22,13,14,20),"t22n15"],
[(1,16,3,19)(2,12)(4,15,11,20)(5,22,10,13)(6,18,9,17)(7,14,8,21),
(1,16,3,20)(2,18)(4,22,11,14)(5,13,10,12)(6,15,9,21)(7,17,8,19),"t22n16"],
[(1,16,6,20,11,13,5,17,10,21,4,14,9,18,3,22,8,15,2,19,7,12),
(1,8,11,6,7,9,2,10,4,3)(12,21,20,14,22,15,17,18,13,16),"t22n17"],
[(1,19,3,12,7,20,4,14,9,13,8,22,6,18,2,21,5,16,11,17)(10,15),
(1,19,4,20,6,17,11,15,7,21,8,14,5,13,3,16,9,18,2,12)(10,22),"t22n18"],
[(1,2,6,11,9)(3,10,5,7,4)(13,15,21,17,16)(14,18,19,22,20),
(1,14,5,20)(2,21,4,13)(3,17)(6,16,11,18)(7,12,10,22)(8,19,9,15),
(1,5)(2,4)(6,11)(7,10)(8,9)(12,15,18,21,13,16,19,22,14,17,20),"t22n19"],
[(1,20,6,19,8,12,11,18,10,16,3,13,9,14,7,21,4,15,5,17)(2,22),
(1,2,8,11,7,5,4,9,6,10)(12,15,19,17,18)(13,20,22,21,16),"t22n20"],
[(2,10,5,4,6)(3,8,9,7,11)(13,17,15,16,21)(14,22,18,20,19),
(1,16,10,17,4,20,8,18,9,12)(2,21)(3,15,5,14,11,22,7,13,6,19),"t22n21"],
[(1,22,15,4,20)(2,21,16,3,19)(5,12,14,9,8)(6,11,13,10,7),
(1,11,3,19,14)(2,12,4,20,13)(5,17,16,9,7)(6,18,15,10,8),"t22n22"],
[(1,4,6,8,10,12,14,15,17,20,21)(2,3,5,7,9,11,13,16,18,19,22),
(1,11,21,10,19,8,18,6,15,3,14)(2,12,22,9,20,7,17,5,16,4,13),"t22n23"],
[(1,6,10,11,3)(2,9,8,5,7)(12,18,15,22,13)(14,17,21,19,20),
(1,22)(2,14,9,13,10,16,7,18,5,12,11,19,4,20,3,17,6,15,8,21),"t22n24"],
[(1,8,3,5,2)(4,9,7,10,11)(12,22,13,20,17)(14,18,21,15,16),
(1,22,6,18,10,17,11,14,3,16)(2,19,9,20,8,12,5,21,7,15)(4,13),
(1,10)(2,9)(3,8)(4,7)(5,6)(12,14,19,15,16,13,22,17,21,20),"t22n25"],
[(1,21,14,15,10,8,12,3)(2,22,13,16,9,7,11,4)(5,20,6,19)(17,18),
(1,3,5,11,18,2,4,6,12,17)(7,16,20,22,14,8,15,19,21,13)(9,10),"t22n26"],
[(1,4,10,5,19,22)(2,3,9,6,20,21)(7,17,13,8,18,14)(11,15)(12,16),
(1,22,17,16,12,5,3,7,14,9,19,2,21,18,15,11,6,4,8,13,10,20),"t22n27"],
[(1,14,4,15,6,18,7,20,10,21,11)(2,13,3,16,5,17,8,19,9,22,12),
(1,9,17,4,11,20,6,13,21,7,16,2,10,18,3,12,19,5,14,22,8,15),"t22n28"],
[(1,13,4,16,6,17,8,19,9,22,11)(2,14,3,15,5,18,7,20,10,21,12),
(1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16,8,15)(9,13)(10,14),"t22n29"],
[(1,9)(2,10)(3,7)(4,8)(11,22,12,21)(13,20)(14,19)(15,17,16,18),
(1,22,19,17,15,14,11,10,7,6,4)(2,21,20,18,16,13,12,9,8,5,3),"t22n30"],
[(1,17,2,16,3,15,4,14,5,13,6,12,7,22,8,21,9,20,10,19,11,18),
(1,6,4,7,8)(2,10,9,5,11)(12,21,17,20,15,16,18,22,19,13),"t22n31"],
[(1,4)(2,3)(5,21)(6,22)(7,19,8,20)(9,18,10,17)(11,16,12,15)(13,14),
(1,6)(2,5)(7,22)(8,21)(9,20,10,19)(11,17)(12,18)(13,16)(14,15),"t22n32"],
[(1,2)(3,12,7,9,19)(4,11,8,10,20)(5,22,14,18,15,6,21,13,17,16),
(1,3,10,6,15)(2,4,9,5,16)(7,21,20,13,18,8,22,19,14,17)(11,12),"t22n33"],
[(3,16,12,6,7,22,10,13,20,17)(4,15,11,5,8,21,9,14,19,18),
(1,15,14,7,12,2,16,13,8,11)(3,21,9,18,20)(4,22,10,17,19)(5,6),"t22n34"],
[(3,5,10,18,12,22,20,16,7,14,4,6,9,17,11,21,19,15,8,13),
(1,5,18,9,7,2,6,17,10,8)(3,12,14,20,16)(4,11,13,19,15)(21,22),"t22n35"],
[(1,15,5,10,4,2,16,6,9,3)(7,17,14,19,22,8,18,13,20,21)(11,12),
(1,6,19,14,4)(2,5,20,13,3)(7,15,21,10,12,8,16,22,9,11),"t22n36"],
[(1,3,14,19,6)(2,4,13,20,5)(7,11,9,21,16)(8,12,10,22,15)(17,18),
(1,11,3,5,22,18,7,16,13,20)(2,12,4,6,21,17,8,15,14,19)(9,10),"t22n37"],
[(1,17,9,5,10,22,8)(3,20,15,12,19,11,14)(4,21,16,13,7,18,6),
(1,5,10)(2,17,12)(3,8,4)(6,16,19)(9,18,21)(14,20,22),"t22n38"],
[(1,9,12,13,17,2,10,11,14,18)(3,22,19,6,8)(4,21,20,5,7)(15,16),
(1,7,6,2,8,5)(3,4)(9,21,18)(10,22,17)(11,15,13,12,16,14)(19,20),"t22n39"],
[(2,4,9,6,3)(5,11,8,7,10)(12,13,20)(14,17,18,22,21,19)(15,16),
(1,13,3,12,6,18,9,17,7,21,8,14,10,15,4,20,5,19,11,22,2,16),"t22n40"],
[(1,15,18,2,9,20,13,21,17,3,4,16)(5,12,22,11,8,14)(6,10,19,7),
(1,22,17,12,15)(2,5,8,20,21)(3,16,11,9,7)(4,10,6,13,18),"t22n41"],
[(3,9,17,19,22,4,10,18,20,21)(5,14,16,11,7)(6,13,15,12,8),
(1,8)(2,7)(3,14)(4,13)(5,10)(6,9)(15,20,16,19)(17,18)(21,22),"t22n42"],
[(1,9,16,19,14,12,18,4,6,22,8)(2,10,15,20,13,11,17,3,5,21,7),
(1,21,17,20)(2,22,18,19)(3,5,8,16,4,6,7,15)(9,10)(11,12)(13,14),"t22n43"],
[(1,15,7,13,11,10,17,4,2,16,8,14,12,9,18,3)(5,19)(6,20),
(1,21,10,18,11,15,5,4,2,22,9,17,12,16,6,3)(7,8)(13,19)(14,20),"t22n44"],
[(1,22,20,18,4,7,9,11,5,14)(2,21,19,17,3,8,10,12,6,13)(15,16),
(1,4,20,12,9,17,5)(2,3,19,11,10,18,6)(7,15,14)(8,16,13),"t22n45"],
[(1,5,13,21,19,18,7,16,9,11,4)(2,6,14,22,20,17,8,15,10,12,3),
(1,2)(3,4)(5,15,19,14,11,22,7,17,9,6,16,20,13,12,21,8,18,10),"t22n46"],
[(1,13,20,22,18,7,4,16,10,11,6,2,14,19,21,17,8,3,15,9,12,5),
(1,15,10,8,6,20,12)(2,16,9,7,5,19,11)(3,17,22,13)(4,18,21,14),"t22n47"],
[(1,16,2,14,11,17,8,18,6,15,9,20)(3,22,10,19)(4,21,7,13,5,12),
(1,16,6,19,9,20,11,17,5,14,8,22,4,13,3,12)(2,18)(7,15,10,21),"t22n48"],
[(1,16,13,6,3,10,22)(2,15,14,5,4,9,21)(7,11)(8,12)(17,20)(18,19),
(1,17,3,10,12,6,7,2,18,4,9,11,5,8)(13,19,15)(14,20,16)(21,22),"t22n49"],
[(3,13,7,22,9,12,17,4,14,8,21,10,11,18)(5,6)(15,20,16,19),
(1,4,21,19,7,2,3,22,20,8)(5,17,15,11,6,18,16,12)(9,10),"t22n50"],
[(1,17,11,3,13,5,16)(2,18,12,4,14,6,15)(7,19,22,10)(8,20,21,9),
(1,14,5,21,11,7,10)(2,13,6,22,12,8,9)(3,19)(4,20)(15,16)(17,18),"t22n51"],
[(1,10,21,19,4,15,11)(2,9,22,20,3,16,12)(5,8,14,6,7,13)(17,18),
(1,14)(2,13)(3,9,16,8,19)(4,10,15,7,20)(5,18,6,17),"t22n52"],
[(1,11,5,4,22,17,20,9)(2,12,6,3,21,18,19,10)(7,16,8,15)(13,14),
(1,12,4,20,17,14)(2,11,3,19,18,13)(5,15,8,21,6,16,7,22),
(1,12,4,13,2,11,3,14)(5,7,21,19,6,8,22,20)(9,17)(10,18)(15,16),"t22n53"],
[(1,21,6,18,4,17,7,16,11,19,3,14,9,15,2,20)(5,12)(8,22,10,13),
(1,21,11,14,2,16,8,13,7,20,5,22,4,12,10,15,6,17,3,18,9,19),"t22n54"],
[(1,21,6,22,7,12,5,15,8,19,3,14,10,18,9,17)(2,20)(4,16)(11,13),
(1,18)(2,16,5,20,6,17,9,12,8,13,11,22,7,21,10,14,4,19,3,15),"t22n55"],
[(1,16)(2,22,10,12,6,18,5,20,9,19,11,17,7,14,3,21,8,15)(4,13),
(1,6,5,3,7,9)(2,8,4,10,11)(12,21,19,14,13)(15,16,18,20,17,22),"t22n56"],
[(1,12,10,15,4,16,3,22,9,13,8,21)(2,19,6,14,7,18)(5,17,11,20),
(1,19,11,22,9,18)(2,15,4,21,3,16,8,13,10,20,7,17,5,14,6,12),"t22n57"],
[(1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22),(1,2,3),"t22n58"],
[(1,2),(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22),"t22n59"]];
TRANSPROPERTIES[22]{[1..59]}:=
[
[22,0,1,-1,
"0020s6904s1180"
,[-9022,11],[-20022],[-69022]],
[22,0,1,-1,
"0020s6904"
,[-10011,-4022],[-20022],[-69022]],
[44,0,1,-1,
"0060s6904s1180"
,[-9022,-11],[-22,9044],[-9022,29044]],
[110,0,1,-1,
"0020s1D08s4404s0604"
,[-1055,-110,-11],[-3110,-22],[-13110]],
[110,0,1,-1,
"0020s1D08s4404s0604s1180"
,[-1110,11],[-3110,-22],[-13110]],
[220,0,1,-1,
"0060s1D08s440Cs0604s1180"
,[-1110,-11],[-22,1220],[-1110,5220]],
[242,0,1,-1,
"0020s6202s0604s1180"
,[-4022,-121],[-9022,-242],[-14022,-4242]],
[484,0,1,1,
"0040s0E02s5302s0604"
,[121,4022],[-4044,-242],[-4242,-4044,4022]],
[484,0,1,-1,
"0060s6202s0604s1180"
,[-4022,-121],[-242,4044],[-4242,-4022,4044]],
[968,0,1,-1,
"0860s0E02s530210s0504s1180"
,[-4022,-121],[-4044,-242],[-4242,-4044,-4022]],
[1210,0,1,-1,
"0020s1D08s4406s0604s1180"
,[-121,-110],[-1110,-242],[-2110,-1210]],
[1210,0,1,-1,
"0020s1D08s4402s0604s1180"
,[-121,-110],[-1110,-242],[-2110,-1210]],
[1320,0,1,-1,
"0120s0301s1908s0D01s0210s3304s0604s1180"
,[-1110,11],[-22,1220],[-330,-110,660,1220]],
[1320,0,1,-1,
"0120s0301s0A40s0E08s0D01s3604s0604s0480"
,[-110,-55,66],[-110,132,220],[-330,-110,660,1220]],
[2420,0,1,-1,
"0060s1D08s440Es0604s1180"
,[-121,-110],[-242,220],[-1210,-110,220]],
[2420,0,1,1,
"0040s0E02s0E08s440As0604"
,[110,121],[-242,-220],[-1210,-220,110]],
[2420,0,1,-1,
"0060s1D08s440As0604s1180"
,[-121,-110],[-242,220],[-1210,-110,220]],
[2420,0,1,1,
"0040s0E02s0E08s440As0604s1002"
,[110,121],[-242,-220],[-1210,-220,110]],
[4840,0,1,-1,
"0860s0E02s0E08s4180s020A10s0504s1180"
,[-121,-110],[-242,-220],[-1210,-220,-110]],
[4840,0,1,-1,
"0860s0E02s0E08s4180s020E10s0504s100280"
,[-121,-110],[-242,-220],[-1210,-220,-110]],
[6050,0,1,-1,
"0020s1701s0508s4406s04200004s1180"
,[-121,-110],[-1110,-242],[-2110,-1210]],
[7920,0,1,1,
"01s0401s0A80s0E08s0D01s2120s1B04"
,[11,220],[22,440],[220,1660]],
[11264,0,1,1,
"5540s6904"
,[11,4044],[22,9044],[9022,14088]],
[12100,0,1,1,
"0040s0E02s0801s0508s3C80s070As04200004s1002"
,[110,121],[-242,-220],[-1210,-220,110]],
[12100,0,1,-1,
"0060s1701s0508s3C80s070Es04200004s1180"
,[-121,-110],[-242,220],[-1210,-110,220]],
[15840,0,1,-1,
"0120s0301s090180s0E08s0D01s0210s1E60s1404s0604s1180"
,[11,220],[-22,440],[220,1320]],
[15840,0,1,-1,
"0120s0301s090240s0E08s0D01s0210s1D0Cs1504s0604s1180"
,[-1110,11],[-22,1220],[-990,-330,220]],
[22528,0,1,-1,
"FFE0s6904s1180"
,[11,4044],[-22,9044],[-9022,14088]],
[22528,0,1,-1,
"5560s0510s0301s02080044s5A04"
,[-4044,-11],[-22,4088],[4044,4088,4176]],
[22528,0,1,1,
"5540s0508s0302s02040082s5A04"
,[-4044,-11],[22,4088],[4044,4088,4176]],
[24200,0,1,-1,
"0860s0E02s080108s0408s3B1080s0480s020E10s0320000Cs100280"
,[-121,-110],[-242,-220],[-1210,-220,-110]],
[45056,0,1,-1,
"FFE0s0518s0303s020C00C6s5A04s1180"
,[-4044,-11],[-22,4088],[4044,4088,4176]],
[56320,0,1,1,
"5540s1D08s4140s0208s0604"
,[11,220],[22,1220],[1110,2440]],
[112640,0,1,1,
"5540s0508s0302s02040082s0E08s4140s0208s0604s1002"
,[-220,-11],[22,440],[220,440,880]],
[112640,0,1,-1,
"5560s0510s0301s02080044s0E08s4140s020Cs0604s1004"
,[-220,-11],[-22,440],[220,440,880]],
[112640,0,1,-1,
"FFE0s1D0Cs41C0s020Cs0604s1180"
,[11,220],[-22,1220],[-1110,2440]],
[225280,0,1,-1,
"FFE0s0518s0303s020C00C6s0E0Cs41C0s020Cs0604s100680"
,[-220,-11],[-22,440],[220,440,880]],
[443520,1,3,1,
"01s0401s0A80s0E08s0D01s1380s0D20s1B04"
,[231],[462],[1540]],
[675840,0,1,1,
"5540s03014028s030As02140280s0E08s0340s0905s0224s3040s0208s0604s022002"
,[11,220],[22,440],[220,440,880]],
[871200,0,1,-1,
"112000022001s0A40s08011001s030800880040s07020001s0210s33062008s02210004s0480s\
0C80"
,[-121,-110],[-242,220],[-1210,-110,220]],
[887040,1,3,-1,
"0320s0301s0901C0s0E08s0D03s1380s0D60s1404s0604s0480s0620"
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