Finite Group Databasebeta

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C₃₇×#544 #14557209

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

206 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)(40,44)(41,43)(42,45)(46,47,49,51)(48,52,53,50);(38,39,41,43)(40,42,45,44);(38,39)(40,42)(41,43)(44,45)(46,48,49,53)(47,50,51,52);(38,40)(39,42)(41,45)(43,44)

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, 225);