Finite Group Databasebeta

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C₂₃×#3137 #15670756

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

372 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 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)(32,33,37,39)(34,40,41,47)(35,36,43,44)(38,45,46,42);(25,28)(29,31)(32,34,36,42,37,41,44,45)(33,38,35,40,39,46,43,47);(24,26,27,30)(25,29,28,31)(32,35,36,39,37,43,44,33)(34,40,42,46,41,47,45,38);(34,41)(38,46)(40,47)(42,45)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1869);