Finite Group Databasebeta

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C₂₉×#3333 #16817047

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

398 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)(30,31,33,35)(32,36,37,34)(38,39,43,47)(40,48,49,53)(41,46,42,45)(44,51,52,50);(30,32)(31,34)(33,37)(35,36)(40,49)(44,52)(48,53)(50,51);(38,40,43,49)(39,44,47,52)(41,50,42,51)(45,48,46,53);(32,37)(34,36)(38,41,43,42)(39,45,47,46)(40,50,49,51)(44,48,52,53)

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, 2065);