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C₂×#35821 #7629180

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

Aliases

Subgroups

12404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536376);