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C₂₃×#1658 #15669277

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

182 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)(25,30)(26,33)(27,28)(32,35)(34,36)(37,38)(41,45)(43,50)(46,54)(47,51)(48,52)(53,55);(24,25)(26,31)(27,35)(28,30)(29,32)(33,38)(34,39)(36,37)(40,41,44,47)(42,46,49,55)(43,51,50,45)(48,53,52,54);(24,26,29,34)(25,31,32,39)(27,33,28,36)(30,37,35,38)(40,42,44,49)(41,46,47,55)(43,52,50,48)(45,53,51,54)

Conjugacy classes & character table

460 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 390);