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C₂×#11006 #357491

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

Aliases

Subgroups

5126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264687);