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D13287 #40997990
Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 149 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);(2,3)(5,46)(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)(48,149)(49,148)(50,147)(51,146)(52,145)(53,144)(54,143)(55,142)(56,141)(57,140)(58,139)(59,138)(60,137)(61,136)(62,135)(63,134)(64,133)(65,132)(66,131)(67,130)(68,129)(69,128)(70,127)(71,126)(72,125)(73,124)(74,123)(75,122)(76,121)(77,120)(78,119)(79,118)(80,117)(81,116)(82,115)(83,114)(84,113)(85,112)(86,111)(87,110)(88,109)(89,108)(90,107)(91,106)(92,105)(93,104)(94,103)(95,102)(96,101)(97,100)(98,99)
Polycyclic presentation:
2,3,43,103|b^a=b^2,c^a=c^42,d^a=d^102
Conjugacy classes & character table
6645 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26574, 12);
Finite Group Databasebeta