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C₂×#446 #2959

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

Aliases

Subgroups

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 18 points:

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

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 1691);