Finite Group Databasebeta

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C₂₃×#3489 #15671108

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,27)(28,29,33,34)(30,36,38,31)(32,40,41,35)(37,39,43,42);(29,34)(31,36)(35,40)(39,42);(24,25)(26,27)(28,30)(29,31)(32,37)(33,38)(34,36)(35,39)(40,42)(41,43);(28,31)(29,30)(32,39)(33,36)(34,38)(35,37)(40,43)(41,42);(28,32,33,41)(29,35,34,40)(30,37,38,43)(31,39,36,42)

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, 2221);