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C₂×#36126 #7629751

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

Aliases

Subgroups

12414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 18 points:

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

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, 7536947);