Finite Group Databasebeta

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C₂₃×#2806 #15670425

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

392 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)(25,28)(26,30)(33,34)(37,38)(40,41,44,45)(42,46,47,43);(25,28)(29,31)(32,33,36,34)(35,38,39,37)(40,42,44,47)(41,43,45,46);(24,25)(26,29)(27,28)(30,31)(32,34,36,33)(35,38,39,37)(40,42)(41,43)(44,47)(45,46);(24,26,27,30)(25,29,28,31)(32,35)(33,37)(34,38)(36,39)(40,43)(41,42)(44,46)(45,47)

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, 1538);