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C₂×#13813 #513481

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

Aliases

Subgroups

10546 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 18 points:

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420677);