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C₂₉×#2245 #16815959

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 69 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)(32,35)(33,34)(36,37)(38,39,45,51)(40,47,55,66)(41,46,57,64)(42,49,59,61)(43,48,52,67)(44,60,58,50)(53,65,68,63)(54,69,56,62);(31,34)(35,37)(38,40,52,68,44,54,42,41,45,55,43,53,58,56,59,57)(39,46,61,69,50,63,48,47,51,64,49,62,60,65,67,66);(30,32,33,36)(31,35,34,37)(38,41,42,56,58,68,52,55,45,57,59,54,44,53,43,40)(39,47,48,65,60,69,61,64,51,66,67,63,50,62,49,46)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 977);