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C₂₃×#3156 #15670775

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

532 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)(25,27)(28,29,33,37)(30,38,42,52)(31,35,43,49)(32,45,39,36)(34,46,48,41)(40,51,54,59)(44,56,53,50)(47,57,58,55);(28,30,39,46,33,42,32,41)(29,34,45,52,37,48,36,38)(31,40,53,57,43,54,44,55)(35,47,56,59,49,58,50,51);(24,25,26,27)(28,31)(29,35)(30,40)(32,44)(33,43)(34,47)(36,50)(37,49)(38,51)(39,53)(41,55)(42,54)(45,56)(46,57)(48,58)(52,59);(31,43)(35,49)(40,54)(44,53)(47,58)(50,56)(51,59)(55,57)

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, 1888);