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C₂×#33557 #7622869

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

Aliases

Subgroups

4228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530065);