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C₂₃×#3564 #15671183

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

936 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 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)(24,25,29,33)(26,34,35,31)(27,38,41,32)(28,30,40,44)(36,46,48,47)(37,45,49,42)(39,52,53,43)(50,55,51,54);(25,30)(26,35)(27,39)(31,45)(33,44)(34,42)(36,50)(37,49)(41,53)(46,47)(48,51)(54,55);(24,26,28,37)(25,31,30,42)(27,36,39,51)(29,35,40,49)(32,46,43,54)(33,34,44,45)(38,47,52,55)(41,48,53,50);(24,27,40,53)(25,32,44,52)(26,36,49,50)(28,39,29,41)(30,43,33,38)(31,46,45,55)(34,47,42,54)(35,48,37,51);(25,30)(31,42)(32,43)(33,44)(34,45)(38,52)(46,54)(47,55)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2296);