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C₂×#36091 #7629676

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

Aliases

Subgroups

25556 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536872);