Finite Group Databasebeta

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C₂₃×#3296 #15670915

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

408 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)(34,37)(35,38)(36,40)(39,43)(41,44)(42,46)(45,47);(24,26)(25,28)(27,31)(29,30)(32,34,36,42)(33,37,40,46)(35,41,43,47)(38,44,39,45);(33,38)(35,43)(37,44)(39,40)(41,47)(45,46);(26,31)(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, 2028);