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C₂×#35168 #7628392

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

Aliases

Subgroups

13842 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)(14,15)(16,17);(7,8)(9,10)(12,17)(13,14);(3,4,5,6)(7,8)(9,10)(11,13,16,14)(12,18,17,15);(11,14,16,13)(12,15,17,18);(11,15)(12,13)(14,17)(16,18)

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, 7535588);