Finite Group Databasebeta

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C₂₉×#2960 #16816674

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

364 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)(32,37)(33,35)(34,36)(38,39,41,45,42,44,48,51)(40,43,46,50,47,49,52,53);(30,32,34,33)(31,35,36,37);(30,33,34,32)(31,35,36,37)(38,40,41,46,42,47,48,52)(39,43,45,50,44,49,51,53);(39,44)(43,49)(45,51)(50,53)

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1692);