Finite Group Databasebeta

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C₂₉×#3317 #16817031

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

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, 2049);