Finite Group Databasebeta

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C₁₀₉×#1425 #28358679

• nilpotent
• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

50 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 173 points:

(1,2,5,11,8,13,7,29)(3,14,17,39,20,41,19,51)(4,21,23,52,25,54,24,55)(6,27,26,37,28,56,22,12)(9,30,31,47,33,46,57,16)(10,34,35,44,36,43,53,15)(18,49,48,61,50,64,45,40)(32,42,38,58,59,63,60,62)(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);(1,3,15,42,6,18,23,30,5,17,34,58,26,48,25,47,8,20,44,63,28,50,24,46,7,19,43,62,22,45,4,16)(2,9,21,40,12,32,53,51,29,57,55,64,56,60,36,41,13,33,54,61,37,59,35,39,11,31,52,49,27,38,10,14)

Conjugacy classes & character table

4142 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 157);