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D5461 #24926352
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 170 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)(44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170);(2,43)(3,42)(4,41)(5,40)(6,39)(7,38)(8,37)(9,36)(10,35)(11,34)(12,33)(13,32)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(45,170)(46,169)(47,168)(48,167)(49,166)(50,165)(51,164)(52,163)(53,162)(54,161)(55,160)(56,159)(57,158)(58,157)(59,156)(60,155)(61,154)(62,153)(63,152)(64,151)(65,150)(66,149)(67,148)(68,147)(69,146)(70,145)(71,144)(72,143)(73,142)(74,141)(75,140)(76,139)(77,138)(78,137)(79,136)(80,135)(81,134)(82,133)(83,132)(84,131)(85,130)(86,129)(87,128)(88,127)(89,126)(90,125)(91,124)(92,123)(93,122)(94,121)(95,120)(96,119)(97,118)(98,117)(99,116)(100,115)(101,114)(102,113)(103,112)(104,111)(105,110)(106,109)(107,108)
Polycyclic presentation:
2,43,127|b^a=b^42,c^a=c^126
Conjugacy classes & character table
2732 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10922, 3);
Finite Group Databasebeta