Finite Group Databasebeta

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C₂₉×#3116 #16816830

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

386 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)(38,39,43,47)(40,44,50,53)(41,46,42,45)(48,52,49,51);(31,34)(35,37)(38,40,43,50)(39,44,47,53)(41,48,42,49)(45,51,46,52);(39,45)(41,42)(44,51)(46,47)(48,49)(52,53);(30,32,33,36)(31,35,34,37)(38,41,43,42)(39,46,47,45)(40,48,50,49)(44,52,53,51)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1848);