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C₂×#36149 #7629778

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

Aliases

Subgroups

10530 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536974);