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C₂×#2712 #52134

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

Aliases

Subgroups

1587 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 45122);