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C₂×#3534 #62721

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

Aliases

Subgroups

4083 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)(12,15)(13,17);(4,8)(5,9)(12,15)(16,18);(11,12)(13,16)(14,15)(17,18);(3,5,7,9)(4,6,8,10)(11,13)(12,16)(14,17)(15,18);(3,6)(4,9)(5,8)(7,10)

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, 55709);