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C₂×#34269 #7625558

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

Aliases

Subgroups

13010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532754);