Finite Group Databasebeta

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C₃₇×#552 #14557217

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 53 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)(38,39,42,43)(40,41,44,45)(48,52)(50,53);(39,43)(41,45)(46,47,49,51)(48,50,52,53);(38,40,42,44)(39,41,43,45)(46,48)(47,50)(49,52)(51,53);(38,41)(39,44)(40,43)(42,45)

Conjugacy classes & character table

925 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 233);