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C₂×#36066 #7629667

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

Aliases

Subgroups

14464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536863);