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C₁₀₉×#2955 #28360209

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 141 points:

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

Conjugacy classes & character table

4796 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 1687);