Finite Group Databasebeta

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C₂₉×#3044 #16816758

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

458 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)(31,33)(34,35,39,43)(36,40,45,54)(37,47,49,57)(38,50,52,42)(41,51,56,48)(44,58,59,65)(46,62,61,55)(53,63,64,60);(30,31,32,33)(34,36)(35,40)(37,44)(38,46)(39,45)(41,53)(42,55)(43,54)(47,58)(48,60)(49,59)(50,62)(51,63)(52,61)(56,64)(57,65);(34,37,39,49)(35,41,43,56)(36,44,45,59)(38,51,52,48)(40,53,54,64)(42,57,50,47)(46,63,61,60)(55,65,62,58);(36,45)(40,54)(44,59)(46,61)(53,64)(55,62)(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, 1776);