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C₂₃×#2017 #15669636

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

350 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)(26,35)(27,40)(28,45)(29,33)(30,34)(31,37)(32,43)(36,53)(38,48)(39,47)(41,52)(42,51)(44,50)(46,54)(49,55);(24,26)(25,31)(27,41)(28,38)(29,37)(30,39)(32,49)(33,47)(34,48)(35,45)(36,42)(40,46)(43,54)(44,55)(50,53)(51,52);(24,27)(25,32)(26,36)(28,42)(29,43)(30,44)(31,46)(33,50)(34,51)(35,52)(37,41)(38,55)(39,54)(40,45)(47,49)(48,53)

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, 749);