Finite Group Databasebeta

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C₂₃×#2110 #15669729

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,27,31,28,33,39,47,29,32,40,46,41,48,54,55)(26,34,36,50,37,43,52,45,35,49,38,53,51,30,42,44);(24,26)(25,30,32,43)(27,38)(28,37)(29,35)(31,45,46,44)(33,34,48,49)(36,40)(39,42)(41,51)(47,53,55,50)(52,54);(26,35)(30,43)(34,49)(36,38)(37,51)(42,52)(44,45)(50,53)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 842);