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C₂×#20195 #6359547

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

Aliases

Subgroups

2115 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6266743);