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C₂×#11321 #358370

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

Aliases

Subgroups

1610 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265566);