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C₂×#21005 #6371534

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

Aliases

Subgroups

6570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278730);