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C₂×#21782 #6374199

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

Aliases

Subgroups

4748 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6281395);