← Prev (#27212986) Next (#27212988) →
Dic3376 #27212987
Aliases
Splittings
Subgroups
30 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 275 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)(33,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275);(1,33,17,49)(2,34,18,50)(3,35,19,51)(4,36,20,52)(5,37,21,53)(6,38,22,54)(7,39,23,55)(8,40,24,56)(9,41,25,57)(10,42,26,58)(11,43,27,59)(12,44,28,60)(13,45,29,61)(14,46,30,62)(15,47,31,63)(16,48,32,64)(66,275)(67,274)(68,273)(69,272)(70,271)(71,270)(72,269)(73,268)(74,267)(75,266)(76,265)(77,264)(78,263)(79,262)(80,261)(81,260)(82,259)(83,258)(84,257)(85,256)(86,255)(87,254)(88,253)(89,252)(90,251)(91,250)(92,249)(93,248)(94,247)(95,246)(96,245)(97,244)(98,243)(99,242)(100,241)(101,240)(102,239)(103,238)(104,237)(105,236)(106,235)(107,234)(108,233)(109,232)(110,231)(111,230)(112,229)(113,228)(114,227)(115,226)(116,225)(117,224)(118,223)(119,222)(120,221)(121,220)(122,219)(123,218)(124,217)(125,216)(126,215)(127,214)(128,213)(129,212)(130,211)(131,210)(132,209)(133,208)(134,207)(135,206)(136,205)(137,204)(138,203)(139,202)(140,201)(141,200)(142,199)(143,198)(144,197)(145,196)(146,195)(147,194)(148,193)(149,192)(150,191)(151,190)(152,189)(153,188)(154,187)(155,186)(156,185)(157,184)(158,183)(159,182)(160,181)(161,180)(162,179)(163,178)(164,177)(165,176)(166,175)(167,174)(168,173)(169,172)(170,171)
Polycyclic presentation:
2^6,211|a^2=f,b^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,g^a=g^210,c^b=cd,d^b=de,e^b=ef,g^b=g^210
Conjugacy classes & character table
3379 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13504, 390);
Finite Group Databasebeta