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C₂×#10780 #353455

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

Aliases

Subgroups

4170 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)(9,11)(10,17,19,21)(12,15)(13,16)(14,18,22,20);(7,9,11,16,13,15,12,8)(10,17,18,22,19,21,20,14);(4,6)(7,10)(8,14)(9,17)(11,18)(12,20)(13,19)(15,21)(16,22)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260651);