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C₂×#23912 #6437438

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

Aliases

Subgroups

7090 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6344634);