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C₂×#2678 #52097

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

Aliases

Subgroups

2525 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 45085);