Finite Group Databasebeta

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C₂₃×#3326 #15670945

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

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, 2058);