Finite Group Databasebeta

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C₂×#139742 #72258029

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

Aliases

Subgroups

5201 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

82 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((3,4)(5,8)(6,9)(7,10)(11,14)(12,15)(13,16)(17,18), (1,2), (3,5)(4,8,10,16)(6,12,14,18)(7,13)(9,15)(11,17), (4,9,10,11)(8,15)(12,18)(16,17));