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C₁₆₉⋊C₃ #92785

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

Aliases

Splittings

Subgroups

6 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 169 points:

(2,4,9)(3,7,17)(5,12,27)(6,15,34)(8,20,44)(10,23,21)(11,26,38)(13,30,63)(14,32,53)(16,37,78)(18,40,22)(19,43,39)(24,51,57)(25,54,71)(28,59,47)(29,62,81)(31,66,117)(33,70,123)(35,73,48)(36,76,82)(41,86,58)(42,88,72)(45,77,49)(46,92,83)(50,55,84)(52,97,112)(56,89,85)(60,106,102)(61,109,125)(64,113,93)(65,116,135)(67,87,140)(68,108,94)(69,121,136)(74,129,103)(75,130,126)(79,132,95)(80,107,137)(90,122,104)(91,134,127)(96,110,111)(98,144,159)(99,131,138)(100,139,105)(101,141,128)(114,154,147)(115,157,162)(118,150,165)(119,156,148)(120,160,163)(124,161,142)(133,155,164)(143,158,153)(145,146,166)(149,152,151)(167,168,169);(1,137,81,40,133,27,122,68,108,65,117,100,54,3,89,136,85,157,58,70,120,145,107,64,146,99,8,2,51,135,84,104,57,154,119,34,115,159,132,7,6,96,88,138,62,103,124,160,72,150,114,66,19,16,5,4,165,111,86,102,59,127,71,156,118,44,18,14,11,141,123,110,148,105,76,126,168,155,20,42,33,13,10,97,153,139,147,9,164,125,73,46,63,41,15,25,143,140,152,109,22,131,163,128,92,45,87,36,31,24,12,169,151,49,21,106,162,17,91,112,77,35,53,29,166,161,26,48,149,130,39,116,90,37,75,67,52,28,144,56,95,47,23,83,38,129,80,113,74,32,61,167,78,55,94,50,43,82,158,134,79,121,69,98,60,30,101,142,93)

Polycyclic presentation:

3,13^2|b^13=c,b^a=b^3c^11,c^a=c^3

Conjugacy classes & character table

59 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(507, 1);