Finite Group Databasebeta

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C₃₇×#497 #14557162

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 57 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)(39,41)(42,43,46,49)(44,50,51,57)(45,53,54,48)(47,55,56,52);(42,44,45,52,46,51,54,55)(43,47,48,50,49,56,53,57);(38,39,40,41)(44,51)(47,56)(50,57)(52,55)

Conjugacy classes & character table

592 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 178);