Finite Group Databasebeta

?

← Prev (#6375798) Next (#6375800) →

C₂×#22141 #6375799

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

Aliases

Subgroups

2780 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6282995);