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C₂×#8149 #181891

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

Aliases

Subgroups

1482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 89087);