Finite Group Databasebeta

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C₂₃×#3317 #15670936

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

392 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)(24,25,27,29)(26,30,31,28)(32,33,37,40)(34,41,42,47)(35,39,36,44)(38,45,46,43);(24,26)(25,28)(27,31)(29,30)(34,42)(38,46)(41,47)(43,45);(32,34,37,42)(33,38,40,46)(35,43,36,45)(39,47,44,41);(26,31)(28,30)(32,35,37,36)(33,39,40,44)(34,43,42,45)(38,47,46,41)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2049);