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C₂×#2059 #23550

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

Aliases

Subgroups

619 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 16538);