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C₂×#36145 #7629772

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

Aliases

Subgroups

8306 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536968);