Finite Group Databasebeta

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C₃₇×#495 #14557160

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

130 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)(44,50)(45,53)(46,48)(47,51)(49,54)(52,56)(55,57);(42,44,45,51,46,52,54,57)(43,47,49,50,48,55,53,56);(38,39,40,41)(43,48)(47,55)(49,53)(50,56)

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, 176);