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C₂×#25292 #6448085

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

Aliases

Subgroups

2802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6355281);