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C₂₉×#3137 #16816851

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

372 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)(32,35)(33,34)(36,37)(38,39,43,45)(40,46,47,53)(41,42,49,50)(44,51,52,48);(31,34)(35,37)(38,40,42,48,43,47,50,51)(39,44,41,46,45,52,49,53);(30,32,33,36)(31,35,34,37)(38,41,42,45,43,49,50,39)(40,46,48,52,47,53,51,44);(40,47)(44,52)(46,53)(48,51)

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, 1869);