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C₂×C₃⋊(C₃⋊(D₁₃₁⋊C₅)) #37556094

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 139 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23580, 69);