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C₂×#36138 #7629765

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

Aliases

Subgroups

9874 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

(1,2);(7,8)(9,10)(11,14)(12,13)(16,21)(17,22);(4,6)(8,13)(9,11)(15,16)(17,18)(19,22)(20,21);(3,4)(5,6)(7,9,12,11)(8,10,13,14)(15,17,20,22)(16,18,21,19);(4,6)(7,10)(8,9)(11,13)(12,14)(15,18,20,19)(16,17,21,22);(3,4)(5,6)(7,11,12,9)(8,14,13,10)(15,19,20,18)(16,22,21,17)

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, 7536961);