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C₂×#3513 #62770

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

Aliases

Subgroups

4041 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 18 points:

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

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, 55758);