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C₂×#3508 #62798

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

Aliases

Subgroups

4311 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)(11,12)(13,17)(14,16)(15,18);(4,7)(8,9)(11,12,15,18)(13,16,14,17);(11,13,15,14)(12,16,18,17);(3,4)(5,8)(6,7)(9,10)(11,12)(13,16)(14,17)(15,18);(3,5,6,10)(4,8,7,9)(11,14,15,13)(12,17,18,16)

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, 55786);