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C₂×#23913 #6437442

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

Aliases

Subgroups

6906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344638);