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C₂×#11187 #357943

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

Aliases

Subgroups

3002 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265139);