Finite Group Databasebeta

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C₂₃×#3136 #15670755

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

404 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)(26,29)(27,28)(30,31)(33,37)(34,40)(35,42)(38,45)(39,44)(41,46);(25,28)(29,31)(32,33,35,37,36,39,42,44)(34,38,40,43,41,45,46,47);(24,26,27,30)(25,29,28,31)(32,34,35,40,36,41,42,46)(33,38,37,43,39,45,44,47);(33,39)(37,44)(38,45)(43,47)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1868);