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C₂×#62916 #10586258

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

Aliases

Subgroups

38036 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 18 points:

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

Conjugacy classes & character table

146 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493454);