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C₂×#62986 #10586029

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

Aliases

Subgroups

37896 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493225);