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C₂×#3481 #62714

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

Aliases

Subgroups

4361 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55702);