Finite Group Databasebeta

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C₃₇×#542 #14557207

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

216 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)(48,52)(50,53);(38,39,41,43)(40,42,45,44)(46,47,49,51)(48,50,52,53);(38,39)(40,42)(41,43)(44,45)(46,48)(47,50)(49,52)(51,53);(38,40,41,45)(39,42,43,44)

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, 223);