Finite Group Databasebeta

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C₂₃×#3385 #15671004

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

340 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)(24,25,28,27)(26,30,31,29)(32,33,36,40)(34,37,41,45)(35,38,43,39)(42,46,47,44);(24,26,28,31)(25,29,27,30)(32,34)(33,37)(35,42)(36,41)(38,46)(39,44)(40,45)(43,47);(33,38)(34,41)(35,43)(37,44)(39,40)(45,46);(24,27,28,25)(26,29,31,30)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2117);