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C₂₃×#2833 #15670452

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 55 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)(29,31)(32,33,36,37)(34,38,39,35)(41,45)(46,48)(47,51)(54,55);(26,30)(29,31)(34,39)(35,38)(40,41,44,45)(42,48,50,46)(43,51,53,47)(49,54,52,55);(24,25)(26,29)(27,28)(30,31)(32,34)(33,35)(36,39)(37,38)(40,42,44,50)(41,46,45,48)(43,52,53,49)(47,55,51,54);(24,26)(25,29)(27,30)(28,31)(32,35)(33,34)(36,38)(37,39)(40,43,44,53)(41,47,45,51)(42,49,50,52)(46,54,48,55)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1565);