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C₃⋊#19154246 #31776138

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

Aliases

Splittings

Subgroups

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 149 points:

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

Polycyclic presentation:

2,3^2,7,139|c^a=c^2,e^a=e^138,d^b=d^2,e^b=e^42

Conjugacy classes & character table

498 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17514, 51);