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C₂×#11375 #358585

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

Aliases

Subgroups

1738 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265781);