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C₂×#11058 #357705

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

Aliases

Subgroups

3162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264901);