Finite Group Databasebeta

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C₂₉×#3563 #16817277

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

912 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 61 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)(32,39)(33,36)(34,42)(35,38)(37,43)(40,44)(41,45)(46,47,52,55)(48,50,53,49)(51,59,60,54)(56,57,61,58);(30,32,35,33)(31,36,38,39)(34,40,43,41)(37,44,42,45)(46,48,52,53)(47,49,55,50)(51,56,60,61)(54,57,59,58);(30,33,35,32)(31,36,38,39)(34,41,43,40)(37,44,42,45)(46,49,52,50)(47,53,55,48)(51,57,60,58)(54,61,59,56);(30,31)(32,39)(33,36)(34,37)(35,38)(40,45)(41,44)(42,43)(46,50,52,49)(47,48,55,53)(51,58,60,57)(54,56,59,61);(30,34)(31,37)(32,40)(33,41)(35,43)(36,44)(38,42)(39,45)(46,51)(47,54)(48,56)(49,57)(50,58)(52,60)(53,61)(55,59)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2295);