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C₂×#2956 #60180

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

Aliases

Subgroups

1337 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53168);