Finite Group Databasebeta

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C₂₉×#2923 #16816637

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

384 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)(38,39,41,45,42,44,48,51)(40,43,47,50,46,49,52,53);(31,34)(35,37)(38,40)(39,43)(41,47)(42,46)(44,49)(45,50)(48,52)(51,53);(30,32,33,36)(31,35,34,37)(39,44)(43,49)(45,51)(50,53);(40,46)(43,49)(47,52)(50,53)

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1655);