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C₂×#21218 #6371976

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

Aliases

Subgroups

5414 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6279172);