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C₂×#21544 #6372890

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

Aliases

Subgroups

3026 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6280086);