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C₂×#22412 #6379023

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

Aliases

Subgroups

5032 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6286219);