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D₅×C₁₃₉⋊C₃ #16861981

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

Aliases

Splittings

Subgroups

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 144 points:

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

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4170, 11);