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C₁₀₇×#2956 #28333639

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

458 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 123 points:

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

Conjugacy classes & character table

4708 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 1688);