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C₂×#2685 #52105

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

Aliases

Subgroups

2049 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)(15,16,18,21)(17,20,22,19);(4,6)(8,11)(9,13)(15,17,18,22)(16,19,21,20);(3,4)(5,6)(7,8)(9,12)(10,11)(13,14)(15,17)(16,20)(18,22)(19,21);(7,9)(8,12)(10,13)(11,14)(15,16)(17,20)(18,21)(19,22)

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, 45093);