Finite Group Databasebeta

?

← Prev (#60164) Next (#60166) →

C₂×#2951 #60165

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

Aliases

Subgroups

1403 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

(1,2);(3,4,6,5)(7,8)(9,14)(10,16)(11,15)(12,17)(13,18)(19,22)(20,21);(7,9)(8,13)(10,18)(11,20)(12,19)(14,15)(16,22)(17,21);(3,5,6,4)(7,9)(8,14)(10,20)(11,18)(12,19)(13,15)(16,21)(17,22);(7,10,12,11)(8,15,17,16)(9,18,19,20)(13,14,21,22)

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53153);