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C₂×#24261 #6442720

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

Aliases

Subgroups

5218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6349916);