Finite Group Databasebeta

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C₃₇×#543 #14557208

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

242 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)(38,39,42,45)(40,46,48,44)(41,43,49,51)(47,52,53,50);(39,43)(40,47)(45,51)(48,53);(38,40,42,48)(39,44,45,46)(41,47,49,53)(43,50,51,52);(39,43)(44,50)(45,51)(46,52)

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, 224);