Finite Group Databasebeta

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C₂₃×#3486 #15671105

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1492 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)(29,33)(31,39)(34,36)(37,43);(28,29,32,33)(30,36,38,34)(31,35,39,40)(37,42,43,41);(24,25)(26,27);(28,30,32,38)(29,34,33,36)(31,37,39,43)(35,41,40,42);(28,31)(29,35)(30,37)(32,39)(33,40)(34,41)(36,42)(38,43)

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, 2218);