Finite Group Databasebeta

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C₂₉×#3111 #16816825

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

392 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)(40,48)(41,46)(42,47)(43,45)(44,50)(49,52)(51,53);(31,34)(35,37)(38,40,42,50)(39,44,47,48)(41,49,43,51)(45,52,46,53);(39,45)(41,43)(44,52)(46,47)(48,53)(49,51);(30,32,33,36)(31,35,34,37)(38,41,42,43)(39,46,47,45)(40,49,50,51)(44,53,48,52)

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, 1843);