Finite Group Databasebeta

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C₂₉×#3117 #16816831

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

386 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)(38,39)(40,46)(41,43)(42,50)(44,48)(45,49)(47,53)(51,52);(31,34)(35,37)(39,43)(44,52)(45,50)(46,53);(38,40,41,47)(39,44,43,52)(42,51,49,48)(45,53,50,46);(30,32,33,36)(31,35,34,37)(40,47)(44,52)(46,53)(48,51)

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, 1849);