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Dic6751 #41008849
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 204 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)(48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204);(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)(49,204)(50,203)(51,202)(52,201)(53,200)(54,199)(55,198)(56,197)(57,196)(58,195)(59,194)(60,193)(61,192)(62,191)(63,190)(64,189)(65,188)(66,187)(67,186)(68,185)(69,184)(70,183)(71,182)(72,181)(73,180)(74,179)(75,178)(76,177)(77,176)(78,175)(79,174)(80,173)(81,172)(82,171)(83,170)(84,169)(85,168)(86,167)(87,166)(88,165)(89,164)(90,163)(91,162)(92,161)(93,160)(94,159)(95,158)(96,157)(97,156)(98,155)(99,154)(100,153)(101,152)(102,151)(103,150)(104,149)(105,148)(106,147)(107,146)(108,145)(109,144)(110,143)(111,142)(112,141)(113,140)(114,139)(115,138)(116,137)(117,136)(118,135)(119,134)(120,133)(121,132)(122,131)(123,130)(124,129)(125,128)(126,127)
Polycyclic presentation:
2,43,157,2|a^2=d,b^a=b^42,c^a=c^156
Conjugacy classes & character table
6754 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27004, 4);
Finite Group Databasebeta