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C₂×#33129 #6629719

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

Aliases

Subgroups

3086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6536915);