Finite Group Databasebeta

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C₂₉×#3314 #16817028

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

410 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)(38,39,42,46)(40,43,47,51)(41,44,49,45)(48,52,53,50);(30,32)(31,34)(33,37)(35,36)(38,40)(39,43)(41,48)(42,47)(44,52)(45,50)(46,51)(49,53);(39,44)(40,47)(41,49)(43,50)(45,46)(51,52);(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, 2046);