Finite Group Databasebeta

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C₂₉×#3018 #16816732

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

724 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)(30,31)(32,39)(33,37)(34,42)(35,38)(36,40)(41,44)(43,45);(30,32)(31,36)(33,40)(34,43)(35,41)(37,44)(38,45)(39,42);(30,31)(32,36)(33,37)(34,42)(35,38)(39,43)(40,44)(41,45);(30,33,35,34)(31,37,38,42)(32,40,41,43)(36,44,45,39)

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, 1750);