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C₂×#45422 #7670067

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

Aliases

Subgroups

12446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7577263);