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C₂×#20202 #6359554

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

Aliases

Subgroups

2135 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 18 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6266750);