Finite Group Databasebeta

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C₂₉×#3172 #16816886

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

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, 1904);