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C₂×#21241 #6372015

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

Aliases

Subgroups

5174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6279211);