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C₂×#36122 #7629747

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

Aliases

Subgroups

12182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536943);