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C₂×#21213 #6371968

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

Aliases

Subgroups

6490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(7,8)(9,12,16,19)(10,13)(11,14)(15,18,21,22)(17,20);(7,9)(8,12,14,19)(10,15)(11,16)(13,18,20,22)(17,21);(3,4,5,6)(7,10)(8,13)(9,15)(11,17)(12,18)(14,20)(16,21)(19,22);(10,17)(13,20)(15,21)(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, 6279164);