Finite Group Databasebeta

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C₂₉×#3174 #16816888

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

362 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)(40,46)(41,48)(43,49)(45,51)(47,52)(50,53);(31,34)(35,37)(38,39,42,44)(40,43,47,50)(41,45,48,51)(46,49,52,53);(38,40,41,46,42,47,48,52)(39,43,45,49,44,50,51,53);(30,32,33,36)(31,35,34,37)(39,44)(43,50)(45,51)(49,53)

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, 1906);