Finite Group Databasebeta

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C₂₃×#3060 #15670679

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

484 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)(32,41)(33,36)(34,39)(38,42)(40,43);(28,30,32,39,33,40,31,38)(29,34,35,37,36,42,41,43);(25,27)(28,29)(30,34)(31,41)(32,35)(33,36)(37,39)(38,43)(40,42);(28,31,33,32)(29,35,36,41)(30,38,40,39)(34,37,42,43)

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, 1792);