Finite Group Databasebeta

?

← Prev (#357558) Next (#357560) →

C₂×#11004 #357559

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

Aliases

Subgroups

5126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264755);