Finite Group Databasebeta

?

← Prev (#15671181) Next (#15671183) →

C₂₃×#3563 #15671182

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

912 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 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)(26,33)(27,30)(28,36)(29,32)(31,37)(34,38)(35,39)(40,41,46,49)(42,44,47,43)(45,53,54,48)(50,51,55,52);(24,26,29,27)(25,30,32,33)(28,34,37,35)(31,38,36,39)(40,42,46,47)(41,43,49,44)(45,50,54,55)(48,51,53,52);(24,27,29,26)(25,30,32,33)(28,35,37,34)(31,38,36,39)(40,43,46,44)(41,47,49,42)(45,51,54,52)(48,55,53,50);(24,25)(26,33)(27,30)(28,31)(29,32)(34,39)(35,38)(36,37)(40,44,46,43)(41,42,49,47)(45,52,54,51)(48,50,53,55);(24,28)(25,31)(26,34)(27,35)(29,37)(30,38)(32,36)(33,39)(40,45)(41,48)(42,50)(43,51)(44,52)(46,54)(47,55)(49,53)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2295);