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C₃×D₅×C₁₃₉⋊C₃ #27159809

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 147 points:

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

Conjugacy classes & character table

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

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12510, 16);