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C₂₃×#3241 #15670860

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

332 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)(26,32)(27,30)(28,31)(29,34)(33,38)(35,37)(36,39)(40,41)(42,45)(43,46)(44,48)(47,51)(49,53)(50,52)(54,55);(24,26,28,34)(25,29,31,32)(27,35,36,33)(30,38,39,37)(40,42)(41,45)(43,50)(44,49)(46,52)(47,54)(48,53)(51,55);(24,27,28,36)(25,30,31,39)(26,33,34,35)(29,37,32,38)(41,46)(43,51)(45,52)(47,48)(50,55)(53,54);(25,31)(29,32)(30,39)(37,38)(42,49)(45,53)(50,55)(52,54)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1973);