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Dic4687 #34035571
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 156 points:
(1,2)(3,4)(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)(48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156);(1,3,2,4)(6,47)(7,46)(8,45)(9,44)(10,43)(11,42)(12,41)(13,40)(14,39)(15,38)(16,37)(17,36)(18,35)(19,34)(20,33)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)(49,156)(50,155)(51,154)(52,153)(53,152)(54,151)(55,150)(56,149)(57,148)(58,147)(59,146)(60,145)(61,144)(62,143)(63,142)(64,141)(65,140)(66,139)(67,138)(68,137)(69,136)(70,135)(71,134)(72,133)(73,132)(74,131)(75,130)(76,129)(77,128)(78,127)(79,126)(80,125)(81,124)(82,123)(83,122)(84,121)(85,120)(86,119)(87,118)(88,117)(89,116)(90,115)(91,114)(92,113)(93,112)(94,111)(95,110)(96,109)(97,108)(98,107)(99,106)(100,105)(101,104)(102,103)
Polycyclic presentation:
2,43,109,2|a^2=d,b^a=b^42,c^a=c^108
Conjugacy classes & character table
4690 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18748, 4);
Finite Group Databasebeta