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C₂×#20980 #6371493

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

Aliases

Subgroups

6586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278689);