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C₂×#60644 #10575243

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

Aliases

Subgroups

13214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

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, 10482439);