Finite Group Databasebeta

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C₂₉×#3316 #16817030

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

388 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)(38,39,42,45)(40,46,47,53)(41,49,51,44)(43,50,52,48);(30,32)(31,34)(33,37)(35,36)(40,47)(43,52)(46,53)(48,50);(38,40,42,47)(39,43,45,52)(41,50,51,48)(44,53,49,46);(32,37)(34,36)

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, 2048);