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C₂×#22687 #6380158

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

Aliases

Subgroups

2560 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6287354);