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C₂×#20864 #6371296

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

Aliases

Subgroups

4890 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278492);