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C₃₇×#546 #14557211

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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, 227);