← Prev (#29507552) Next (#29507554) →
D7712 #29507553
Aliases
Splittings
Subgroups
34 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 273 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)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273);(2,32)(3,31)(4,30)(5,29)(6,28)(7,27)(8,26)(9,25)(10,24)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)(34,273)(35,272)(36,271)(37,270)(38,269)(39,268)(40,267)(41,266)(42,265)(43,264)(44,263)(45,262)(46,261)(47,260)(48,259)(49,258)(50,257)(51,256)(52,255)(53,254)(54,253)(55,252)(56,251)(57,250)(58,249)(59,248)(60,247)(61,246)(62,245)(63,244)(64,243)(65,242)(66,241)(67,240)(68,239)(69,238)(70,237)(71,236)(72,235)(73,234)(74,233)(75,232)(76,231)(77,230)(78,229)(79,228)(80,227)(81,226)(82,225)(83,224)(84,223)(85,222)(86,221)(87,220)(88,219)(89,218)(90,217)(91,216)(92,215)(93,214)(94,213)(95,212)(96,211)(97,210)(98,209)(99,208)(100,207)(101,206)(102,205)(103,204)(104,203)(105,202)(106,201)(107,200)(108,199)(109,198)(110,197)(111,196)(112,195)(113,194)(114,193)(115,192)(116,191)(117,190)(118,189)(119,188)(120,187)(121,186)(122,185)(123,184)(124,183)(125,182)(126,181)(127,180)(128,179)(129,178)(130,177)(131,176)(132,175)(133,174)(134,173)(135,172)(136,171)(137,170)(138,169)(139,168)(140,167)(141,166)(142,165)(143,164)(144,163)(145,162)(146,161)(147,160)(148,159)(149,158)(150,157)(151,156)(152,155)(153,154)
Polycyclic presentation:
2^6,241|c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,g^a=g^240,c^b=cd,d^b=de,e^b=ef,g^b=g^240
Conjugacy classes & character table
3859 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 385);
Finite Group Databasebeta