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C₂₃×#2821 #15670440

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

430 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 51 points:

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

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, 1553);