Finite Group Databasebeta

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C₂₉×#3365 #16817079

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

348 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)(31,34)(35,36)(38,39,43,46)(40,44,42,50)(41,48,49,52)(45,51,53,47);(30,31,33,34)(32,36,37,35)(38,40,43,42)(39,44,46,50)(41,47,49,51)(45,52,53,48);(38,41,43,49)(39,45,46,53)(40,47,42,51)(44,52,50,48);(30,32,33,37)(31,35,34,36)

Conjugacy classes & character table

1015 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2097);