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C₂×#31414 #7504662

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

Aliases

Subgroups

2127 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7411858);