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C₂×#36127 #7629752

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

Aliases

Subgroups

12290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 18 points:

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

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, 7536948);