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C₂×#36128 #7629753

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

Aliases

Subgroups

13394 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536949);