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C₂₉×#1838 #16815552

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 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)(38,39,43,47,44,48,42,52)(40,49,50,53,51,46,41,45);(31,34)(35,37)(38,40,42,41,44,51,43,50)(39,45,47,49,48,53,52,46);(30,32,33,36)(31,35,34,37)(38,41,42,51,44,50,43,40)(39,46,47,45,48,49,52,53)

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, 570);