Finite Group Databasebeta

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C₂₃×#1837 #15669456

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

188 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 47 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)(26,29)(27,28)(30,31)(32,33,36,42,38,43,37,41)(34,40,35,39,45,46,44,47);(25,28)(29,31)(32,34,37,44,38,45,36,35)(33,39,42,46,43,47,41,40);(24,26,27,30)(25,29,28,31)(32,35,36,45,38,44,37,34)(33,40,41,47,43,46,42,39)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 569);