Finite Group Databasebeta

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C₂₉×#3068 #16816782

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

466 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 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)(31,35)(32,38)(33,41)(37,43)(39,40)(42,45);(30,31,33,35,34,37,41,43)(32,36,39,42,40,44,38,45);(30,32)(31,36)(33,39)(34,40)(35,42)(37,44)(38,41)(43,45);(31,37)(35,43)(36,44)(42,45)

Conjugacy classes & character table

841 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1800);