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C₂×#21071 #6371659

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

Aliases

Subgroups

3334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278855);