Finite Group Databasebeta

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C₂₃×#3116 #15670735

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

386 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 47 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)(26,29)(27,28)(30,31)(32,33,37,41)(34,38,44,47)(35,40,36,39)(42,46,43,45);(25,28)(29,31)(32,34,37,44)(33,38,41,47)(35,42,36,43)(39,45,40,46);(33,39)(35,36)(38,45)(40,41)(42,43)(46,47);(24,26,27,30)(25,29,28,31)(32,35,37,36)(33,40,41,39)(34,42,44,43)(38,46,47,45)

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, 1848);