Finite Group Databasebeta

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C₃₇×#485 #14557150

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

96 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)(40,43)(41,42)(44,45)(46,47,50,54)(48,51,56,60)(49,52,57,53)(55,58,61,59);(39,42)(43,45)(46,48,50,56)(47,51,54,60)(49,55,57,61)(52,58,53,59);(38,40,41,44)(39,43,42,45)(47,52)(49,57)(51,58)(53,54)(55,61)(59,60)

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 166);