Finite Group Databasebeta

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C₂₃×#3220 #15670839

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

420 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 47 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)(34,37)(35,38)(36,40)(39,43)(41,45)(42,44)(46,47);(24,26,27,31)(25,28,29,30)(32,34)(33,37)(35,42)(36,41)(38,44)(39,46)(40,45)(43,47);(26,31)(28,30)(33,38)(35,43)(37,44)(39,40)(42,47)(45,46);(25,29)(28,30)(34,41)(37,45)(42,47)(44,46)

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, 1952);