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C₂₃×#3567 #15671186

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

950 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)(25,29)(26,32)(31,36)(33,38)(40,41)(42,45)(43,48)(44,49)(46,50)(47,52)(51,53)(54,55);(25,29)(30,35)(31,36)(37,39)(41,42)(43,50)(47,49)(51,55);(24,25)(26,30)(27,31)(28,29)(32,35)(33,37)(34,36)(38,39)(40,42,45,41)(43,48,50,46)(44,49,52,47)(51,54,55,53);(24,26,28,32)(25,30,29,35)(27,33,34,38)(31,37,36,39)(40,43)(41,46)(42,48)(44,51)(45,50)(47,53)(49,54)(52,55);(24,27,28,34)(25,31,29,36)(26,33,32,38)(30,37,35,39)(40,44)(41,47)(42,49)(43,51)(45,52)(46,53)(48,54)(50,55)

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, 2299);