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C₂×#59129 #7666322

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

Aliases

Subgroups

12988 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 18 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573518);