Finite Group Databasebeta

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C₂×#846229 #72298723

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

Aliases

Subgroups

81519 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

184 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((7,8)(9,10)(11,12)(13,14)(16,18), (3,4)(5,6)(15,16)(17,18), (4,6)(7,8,9,10)(12,14), (4,6)(8,10)(11,12)(13,14), (3,4)(5,6)(7,8)(9,10), (1,2));