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C₂₃×#3556 #15671175

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

890 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)(24,25,29,27)(26,32,34,30)(28,35,36,31)(33,37,39,38)(40,41,45,49)(42,47,43,46)(44,52,53,48)(50,54,51,55);(24,26,29,34)(25,30,27,32)(28,33,36,39)(31,37,35,38)(40,41)(42,47)(43,46)(44,48)(45,49)(50,55)(51,54)(52,53);(40,42,45,43)(41,46,49,47)(44,50,53,51)(48,54,52,55);(24,27,29,25)(26,30,34,32)(28,35,36,31)(33,37,39,38)(40,43,45,42)(41,47,49,46)(44,51,53,50)(48,55,52,54);(24,28,29,36)(25,31,27,35)(26,33,34,39)(30,37,32,38)(40,44,45,53)(41,48,49,52)(42,50,43,51)(46,54,47,55)

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, 2288);