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C₂×#20961 #6371463

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

Aliases

Subgroups

7178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278659);