Finite Group Databasebeta

?

← Prev (#17991508) Next (#17991510) →

C₃₇×#2691 #17991509

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 57 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)(42,43)(44,45)(46,47)(48,49)(50,51)(52,56)(53,55)(54,57);(39,41)(43,47)(45,48)(50,51,53,55)(52,56,57,54);(38,39)(40,41)(42,44)(43,48)(45,47)(46,49)(50,51)(52,54)(53,55)(56,57);(42,45,46,48)(43,44,47,49)(50,52,53,57)(51,54,55,56)

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1423);