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C₁₀₁×#1837 #27167191

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

188 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 125 points:

(1,2)(3,5)(4,6)(7,8)(9,10,14,18,15,20,13,19)(11,17,21,24,22,23,12,16)(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);(1,3,4,7)(2,5,6,8)(9,11,14,21,15,22,13,12)(10,16,19,23,20,24,18,17);(2,6)(5,8)(9,12,13,22,15,21,14,11)(10,17,18,24,20,23,19,16)

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, 569);