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C₂₃×#2884 #15670503

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

716 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)(26,34,37,30)(27,31)(28,32)(29,33)(35,48,51,42)(36,49,53,43)(38,44)(39,45)(40,46)(41,47)(50,55,52,54);(24,26)(25,30)(27,35)(28,36)(29,37)(31,42)(32,43)(33,34)(38,50)(39,51)(40,52)(41,53)(44,54)(45,48)(46,55)(47,49);(24,27,29,39)(25,31,33,45)(26,35,37,51)(28,40,41,38)(30,42,34,48)(32,46,47,44)(36,52,53,50)(43,55,49,54);(24,28,29,41)(25,32,33,47)(26,36,37,53)(27,38,39,40)(30,43,34,49)(31,44,45,46)(35,50,51,52)(42,54,48,55)

Conjugacy classes & character table

943 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1616);