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C₂×#3514 #62778

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

Aliases

Subgroups

4003 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,10)(6,9)(7,8)(12,15)(16,18);(4,8)(9,10);(3,5,7,6)(4,9,8,10)(11,12)(13,16)(14,15)(17,18);(3,4)(5,9)(6,10)(7,8);(3,6,7,5)(4,10,8,9)(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, 55766);