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C₂×#10939 #354103

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

Aliases

Subgroups

3418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

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, 261299);