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C₂×#25196 #6438900

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

Aliases

Subgroups

3273 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6346096);