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C₂×#28404 #6463122

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

Aliases

Subgroups

3354 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)(9,13)(10,11)(12,14)(15,16,20,22,19,17,18,21);(8,11)(12,13)(15,17,20,21,19,16,18,22);(4,6)(15,17,19,16)(18,21,20,22);(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, 6370318);