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C₂×#36221 #7629868

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

Aliases

Subgroups

11350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7537064);