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C₁₀₁×#2932 #27168286

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 121 points:

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

Conjugacy classes & character table

4444 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 1664);