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C₂×#15226 #608546

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

Aliases

Subgroups

6998 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 515742);