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C₂₃×#3011 #15670630

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

700 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 59 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)(26,27)(28,29,33,37)(30,38,41,51)(31,35,42,49)(32,44,46,36)(34,45,48,40)(39,52,53,59)(43,56,55,50)(47,57,58,54);(28,30,33,41)(29,34,37,48)(31,39,42,53)(32,45,46,40)(35,47,49,58)(36,51,44,38)(43,57,55,54)(50,59,56,52);(25,27)(28,31)(29,35)(30,39)(32,43)(33,42)(34,47)(36,50)(37,49)(38,52)(40,54)(41,53)(44,56)(45,57)(46,55)(48,58)(51,59);(31,42)(35,49)(39,53)(43,55)(47,58)(50,56)(52,59)(54,57)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1743);