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C₂×#20445 #6369906

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

Aliases

Subgroups

3198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6277102);