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C₂₉×#2794 #16816508

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

344 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 53 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)(32,36)(33,34)(35,37)(39,42)(40,44)(46,47,50,52)(48,49,51,53);(31,34)(35,36)(38,39,41,42)(40,45,44,43)(46,48)(47,49)(50,51)(52,53);(30,32,33,37)(31,35,34,36)(46,49)(47,51)(48,52)(50,53);(30,31)(32,35)(33,34)(36,37)(38,40,41,44)(39,43,42,45)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1526);