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C₂×#2723 #52146

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

Aliases

Subgroups

1393 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 45134);