Finite Group Databasebeta

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C₃₇×#491 #14557156

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 61 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)(40,43)(41,42)(44,45)(46,47,52,57)(48,54,59,60)(49,53,58,61)(50,56,51,55);(39,42)(43,45)(46,48,50,49,52,59,51,58)(47,53,55,54,57,61,56,60);(38,40,41,44)(39,43,42,45)(46,49,50,59,52,58,51,48)(47,54,55,61,57,60,56,53)

Conjugacy classes & character table

592 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 172);