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C₂×#28397 #6463127

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

Aliases

Subgroups

3658 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)(9,13)(10,11)(12,14)(15,16,18,21,20,22,19,17);(8,11)(12,13)(15,17,19,22,20,21,18,16);(4,6)(16,17)(18,19)(21,22);(7,9,10,14)(8,12,11,13)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6370323);