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C₂×#9968 #232200

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

Aliases

Subgroups

2248 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 139396);