Finite Group Databasebeta

?

← Prev (#609445) Next (#609447) →

C₂×#15769 #609446

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

Aliases

Subgroups

5266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 516642);