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C₂×#3543 #62744

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

Aliases

Subgroups

4407 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55732);