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C₂₃×#1830 #15669449

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 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)(24,25,28,33,29,32,42,47)(26,34,36,48,37,30,41,44)(27,38,40,52,39,31,45,46)(35,43,51,54,50,49,53,55);(24,26,29,37)(25,30,32,34)(27,35,39,50)(28,41,42,36)(31,43,38,49)(33,48,47,44)(40,53,45,51)(46,55,52,54);(24,27)(25,31,32,38)(26,35)(28,40)(29,39)(30,43,34,49)(33,46,47,52)(36,51)(37,50)(41,53)(42,45)(44,54,48,55)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 562);