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C₂×#28364 #6459728

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

Aliases

Subgroups

3806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6366924);