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C₂×#36022 #7629462

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

Aliases

Subgroups

9810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536658);