Finite Group Databasebeta

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C₂₃×#3364 #15670983

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

336 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)(25,28)(29,30)(32,33)(34,38)(35,42)(36,44)(37,40)(39,41)(43,46)(45,47);(24,25,27,28)(26,30,31,29)(32,34,37,36)(33,38,40,44)(35,41,43,45)(39,46,47,42);(32,35,37,43)(33,39,40,47)(34,41,36,45)(38,46,44,42);(24,26,27,31)(25,29,28,30)

Conjugacy classes & character table

805 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2096);