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Dic₂₈₉₆ #26041120

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 245 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);(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)(66,245)(67,244)(68,243)(69,242)(70,241)(71,240)(72,239)(73,238)(74,237)(75,236)(76,235)(77,234)(78,233)(79,232)(80,231)(81,230)(82,229)(83,228)(84,227)(85,226)(86,225)(87,224)(88,223)(89,222)(90,221)(91,220)(92,219)(93,218)(94,217)(95,216)(96,215)(97,214)(98,213)(99,212)(100,211)(101,210)(102,209)(103,208)(104,207)(105,206)(106,205)(107,204)(108,203)(109,202)(110,201)(111,200)(112,199)(113,198)(114,197)(115,196)(116,195)(117,194)(118,193)(119,192)(120,191)(121,190)(122,189)(123,188)(124,187)(125,186)(126,185)(127,184)(128,183)(129,182)(130,181)(131,180)(132,179)(133,178)(134,177)(135,176)(136,175)(137,174)(138,173)(139,172)(140,171)(141,170)(142,169)(143,168)(144,167)(145,166)(146,165)(147,164)(148,163)(149,162)(150,161)(151,160)(152,159)(153,158)(154,157)(155,156)

Polycyclic presentation:

2^6,181|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^180,c^b=cd,d^b=de,e^b=ef,g^b=g^180

Conjugacy classes & character table

2899 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11584, 390);