Finite Group Databasebeta

?

← Prev (#15670573) Next (#15670575) →

C₂₃×#2955 #15670574

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 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)(24,25,29,34,30,33,28,42)(26,35,37,31,38,46,43,45)(27,32,40,48,41,47,39,52)(36,49,50,44,51,55,53,54);(24,26)(25,31)(27,36)(28,43)(29,37)(30,38)(32,44)(33,45)(34,46)(35,42)(39,53)(40,50)(41,51)(47,54)(48,55)(49,52);(24,27,29,40,30,41,28,39)(25,32,34,48,33,47,42,52)(26,36,37,50,38,51,43,53)(31,44,46,55,45,54,35,49);(25,33)(31,45)(32,47)(34,42)(35,46)(44,54)(48,52)(49,55)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1687);