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C₂₃×#3177 #15670796

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

338 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)(26,29)(27,28)(30,31)(32,33,37,41)(34,38,43,51)(35,45,48,60)(36,49,46,40)(39,53,54,47)(42,55,57,63)(44,59,56,52)(50,61,62,58);(25,28)(29,31)(32,34,37,43)(33,38,41,51)(35,42,48,57)(36,44,46,56)(39,50,54,62)(40,52,49,59)(45,55,60,63)(47,58,53,61);(32,35,46,53,37,48,36,47)(33,39,49,60,41,54,40,45)(34,42,56,61,43,57,44,58)(38,50,59,63,51,62,52,55);(24,26,27,30)(25,29,28,31)(34,43)(38,51)(42,57)(44,56)(50,62)(52,59)(55,63)(58,61)

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, 1909);