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C₂₃×#1534 #15669153

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

196 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)(24,25,27,31,28,30,36,38)(26,32,33,39,34,29,35,37)(40,41)(42,48,50,55)(43,47)(44,46)(45,49,53,51)(52,54);(24,26,28,34)(25,29,30,32)(27,35,36,33)(31,39,38,37)(40,42)(41,45)(43,51)(44,50)(46,53)(47,55)(48,54)(49,52);(41,46)(45,53)(47,54)(48,55)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 266);