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C₂×#11008 #357494

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

Aliases

Subgroups

7850 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,6)(11,12,13,14)(15,16)(17,20)(18,21)(19,22);(4,6)(7,8)(9,10)(16,20)(17,18)(21,22);(8,10)(16,21)(17,18)(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, 264690);