Finite Group Databasebeta

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C₂₉×#3136 #16816850

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

404 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)(39,43)(40,46)(41,48)(44,51)(45,50)(47,52);(31,34)(35,37)(38,39,41,43,42,45,48,50)(40,44,46,49,47,51,52,53);(30,32,33,36)(31,35,34,37)(38,40,41,46,42,47,48,52)(39,44,43,49,45,51,50,53);(39,45)(43,50)(44,51)(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, 1868);