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C₂×#36102 #7629725

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

Aliases

Subgroups

13874 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536921);