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C₂×#15163 #608418

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

Aliases

Subgroups

6102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 515614);