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C₂×#408×C₁₀₁ #27168232

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

5656 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 1610);