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C₂×#23879 #6437468

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

Aliases

Subgroups

6696 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344664);