Finite Group Databasebeta

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C₃₇×#499 #14557164

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

86 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 61 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37)(38,39,41,43)(40,44,45,42)(46,47,49,51)(48,54,55,61)(50,58,57,53)(52,60,59,56);(38,40,41,45)(39,42,43,44)(47,51)(52,59)(53,58)(54,61);(46,48,50,56,49,55,57,60)(47,52,53,54,51,59,58,61)

Conjugacy classes & character table

814 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 180);