Finite Group Databasebeta

?

← Prev (#357561) Next (#357563) →

C₂×#11012 #357562

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

Aliases

Subgroups

4974 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)(9,15,18,12)(10,14)(11,13)(16,21,17,20)(19,22);(7,9)(8,12)(10,16)(11,18)(13,15)(14,20)(17,19)(21,22);(4,6)(9,16)(10,19)(12,20)(14,22)(15,21)(17,18)

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, 264758);