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C₂×#12705 #493388

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

Aliases

Subgroups

4190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 18 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400584);