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Dic4141 #30658583
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 146 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);(1,3,2,4)(6,45)(7,44)(8,43)(9,42)(10,41)(11,40)(12,39)(13,38)(14,37)(15,36)(16,35)(17,34)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)(47,146)(48,145)(49,144)(50,143)(51,142)(52,141)(53,140)(54,139)(55,138)(56,137)(57,136)(58,135)(59,134)(60,133)(61,132)(62,131)(63,130)(64,129)(65,128)(66,127)(67,126)(68,125)(69,124)(70,123)(71,122)(72,121)(73,120)(74,119)(75,118)(76,117)(77,116)(78,115)(79,114)(80,113)(81,112)(82,111)(83,110)(84,109)(85,108)(86,107)(87,106)(88,105)(89,104)(90,103)(91,102)(92,101)(93,100)(94,99)(95,98)(96,97)
Polycyclic presentation:
2,41,101,2|a^2=d,b^a=b^40,c^a=c^100
Conjugacy classes & character table
4144 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16564, 4);
Finite Group Databasebeta