Finite Group Databasebeta

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C₂₃×#3216 #15670835

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

390 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)(32,33,37,40)(34,41,42,47)(35,39,36,44)(38,45,46,43);(24,26,27,31)(25,28,29,30)(34,42)(38,46)(41,47)(43,45);(26,31)(28,30)(32,34)(33,38)(35,43)(36,45)(37,42)(39,47)(40,46)(41,44);(25,29)(28,30)(32,35,37,36)(33,39,40,44)(34,43,42,45)(38,47,46,41)

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, 1948);