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C₂×#36218 #7629865

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

Aliases

Subgroups

12496 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7537061);