Finite Group Databasebeta

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C₂×#759721 #72296861

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

Aliases

Subgroups

99021 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)(15,16)(17,18);(4,6)(8,10)(15,16,17,18);(8,10)(11,12)(13,14)(15,16)(17,18);(8,10)(12,14)(16,18);(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18);(1,2)

Conjugacy classes & character table

208 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)(15,16)(17,18), (4,6)(8,10)(15,16,17,18), (8,10)(11,12)(13,14)(15,16)(17,18), (8,10)(12,14)(16,18), (3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18), (1,2));