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C₂×#35514 #7628892

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

Aliases

Subgroups

13950 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536088);