Finite Group Databasebeta

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C₂₃×#3519 #15671138

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 39 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)(26,30)(27,28)(29,31)(32,33)(34,38)(35,36)(37,39);(25,28)(29,30)(33,36)(37,38);(32,34)(33,37)(35,39)(36,38);(24,25)(26,29)(27,28)(30,31)(32,33)(34,37)(35,36)(38,39);(24,26,27,31)(25,29,28,30)(32,34)(33,37)(35,39)(36,38)

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, 2251);