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C₂×#21473 #6372702

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

Aliases

Subgroups

5084 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6279898);