Finite Group Databasebeta

?

← Prev (#19598) Next (#19600) →

C₂×#1711 #19599

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

401 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4)(5,11)(6,15)(7,9)(8,13)(10,12)(14,17)(16,18)(19,20)(21,27)(22,24)(23,31)(25,29)(26,30)(28,33)(32,34);(3,5,12,18,7,14,6,13)(4,8,15,17,9,16,10,11)(20,24)(25,32)(26,31)(27,33);(4,9)(8,16)(10,15)(11,17)(19,21,23,29,22,28,30,34)(20,25,26,27,24,32,31,33)

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 12587);