Finite Group Databasebeta

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D₁₉₁ #67422

• metacyclic
• supersolvable
• metabelian
• solvable
• monolithic
• monomial
• stem
• Frobenius
• ambivalent

Aliases

Splittings

Subgroups

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 191 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);(2,191)(3,190)(4,189)(5,188)(6,187)(7,186)(8,185)(9,184)(10,183)(11,182)(12,181)(13,180)(14,179)(15,178)(16,177)(17,176)(18,175)(19,174)(20,173)(21,172)(22,171)(23,170)(24,169)(25,168)(26,167)(27,166)(28,165)(29,164)(30,163)(31,162)(32,161)(33,160)(34,159)(35,158)(36,157)(37,156)(38,155)(39,154)(40,153)(41,152)(42,151)(43,150)(44,149)(45,148)(46,147)(47,146)(48,145)(49,144)(50,143)(51,142)(52,141)(53,140)(54,139)(55,138)(56,137)(57,136)(58,135)(59,134)(60,133)(61,132)(62,131)(63,130)(64,129)(65,128)(66,127)(67,126)(68,125)(69,124)(70,123)(71,122)(72,121)(73,120)(74,119)(75,118)(76,117)(77,116)(78,115)(79,114)(80,113)(81,112)(82,111)(83,110)(84,109)(85,108)(86,107)(87,106)(88,105)(89,104)(90,103)(91,102)(92,101)(93,100)(94,99)(95,98)(96,97)

Polycyclic presentation:

2,191|b^a=b^190

Conjugacy classes & character table

97 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(382, 1);