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C₂×#36440 #7630120

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

Aliases

Subgroups

11296 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537316);