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C₂×#20952 #6371449

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

Aliases

Subgroups

6546 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278645);