Finite Group Databasebeta

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C₂₉×#1534 #16815248

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 61 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)(30,31,33,37,34,36,42,44)(32,38,39,45,40,35,41,43)(46,47)(48,54,56,61)(49,53)(50,52)(51,55,59,57)(58,60);(30,32,34,40)(31,35,36,38)(33,41,42,39)(37,45,44,43)(46,48)(47,51)(49,57)(50,56)(52,59)(53,61)(54,60)(55,58);(47,52)(51,59)(53,60)(54,61)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 266);