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C₂₃×#3289 #15670908

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

448 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)(24,25,30,36)(26,37,41,52)(27,33,43,51)(28,35,29,34)(31,44,48,40)(32,45,49,42)(38,46,55,47)(39,53,54,50);(24,26,30,41)(25,31,36,48)(27,38,43,55)(28,44,29,40)(32,46,49,47)(33,50,51,53)(34,52,35,37)(39,45,54,42);(24,27)(25,32)(26,38)(28,42)(29,45)(30,43)(31,46)(33,34)(35,51)(36,49)(37,53)(39,44)(40,54)(41,55)(47,48)(50,52);(24,27)(25,33)(26,39)(28,45)(29,42)(30,43)(31,47)(32,34)(35,49)(36,51)(37,53)(38,44)(40,55)(41,54)(46,48)(50,52)

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, 2021);