Finite Group Databasebeta

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C₂₃×#3005 #15670624

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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, 1737);