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C₂×#23016 #6381898

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

Aliases

Subgroups

2620 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6289094);