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C₂×#11146 #357846

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

Aliases

Subgroups

2798 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265042);