Finite Group Databasebeta

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C₂₉×#2069 #16815783

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 45 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)(30,31,35,37,34,38,33,42)(32,39,43,44,40,45,41,36);(30,32,33,41,34,40,35,43)(31,36,37,39,38,44,42,45);(32,40)(33,35)(37,42)(39,45)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 801);