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C₁₀₉×#3400 #28360654

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

362 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 133 points:

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

Conjugacy classes & character table

3161 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 2132);