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C₂×#3214 #60787

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

Aliases

Subgroups

1223 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 18 points:

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53775);