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C₂₃×#3223 #15670842

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

364 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 63 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)(26,30)(27,29)(28,31)(32,33,37,41)(34,38,43,52)(35,45,47,55)(36,48,50,40)(39,49,54,46)(42,56,57,63)(44,60,59,53)(51,61,62,58);(24,26,27,31)(25,28,29,30)(32,34)(33,38)(35,42)(36,44)(37,43)(39,51)(40,53)(41,52)(45,56)(46,58)(47,57)(48,60)(49,61)(50,59)(54,62)(55,63);(26,31)(28,30)(32,35,37,47)(33,39,41,54)(34,42,43,57)(36,49,50,46)(38,51,52,62)(40,55,48,45)(44,61,59,58)(53,63,60,56);(25,29)(28,30)(34,43)(38,52)(42,57)(44,59)(51,62)(53,60)(56,63)(58,61)

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, 1955);