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C₂×#10987 #357473

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

Aliases

Subgroups

5134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 264669);