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C₂×#11142 #357837

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

Aliases

Subgroups

3154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265033);