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C₂×#34932 #7628100

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

Aliases

Subgroups

8670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535296);