Finite Group Databasebeta

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C₂₉×#3011 #16816725

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

700 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 65 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)(32,33)(34,35,39,43)(36,44,47,57)(37,41,48,55)(38,50,52,42)(40,51,54,46)(45,58,59,65)(49,62,61,56)(53,63,64,60);(34,36,39,47)(35,40,43,54)(37,45,48,59)(38,51,52,46)(41,53,55,64)(42,57,50,44)(49,63,61,60)(56,65,62,58);(31,33)(34,37)(35,41)(36,45)(38,49)(39,48)(40,53)(42,56)(43,55)(44,58)(46,60)(47,59)(50,62)(51,63)(52,61)(54,64)(57,65);(37,48)(41,55)(45,59)(49,61)(53,64)(56,62)(58,65)(60,63)

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, 1743);