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C₂×#14714 #607617

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

Aliases

Subgroups

7050 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 514813);