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C₂×#61068 #10576055

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

Aliases

Subgroups

10738 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483251);