Finite Group Databasebeta

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C₂₃×#2507 #15670126

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

396 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)(26,30)(27,28)(29,31)(33,35)(34,38)(40,41,43,45)(42,46,47,44);(25,28)(29,30)(32,33,36,35)(34,39,38,37)(40,41)(42,44)(43,45)(46,47);(24,25)(26,29)(27,28)(30,31)(32,34,36,38)(33,37,35,39);(24,26,27,31)(25,29,28,30)(32,35,36,33)(34,39,38,37)(40,42,43,47)(41,44,45,46)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1239);