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C₂×#13153 #494922

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

Aliases

Subgroups

816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402118);