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C₂×#36187 #7629824

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

Aliases

Subgroups

9098 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)(9,13,14,11)(15,16,19,21)(17,18,20,22);(7,9)(8,11)(10,13)(12,14)(15,17)(16,18)(19,20)(21,22);(3,4,5,6)(8,10)(9,14)(15,18)(16,20)(17,21)(19,22);(7,10,12,8)(9,13,14,11)(15,17)(16,18)(19,20)(21,22);(7,11,12,13)(8,9,10,14)(15,18)(16,20)(17,21)(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, 7537020);