Finite Group Databasebeta

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C₂×#783582 #72302576

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

Aliases

Subgroups

46663 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

(1,2)(4,5)(8,10)(11,12)(13,14);(7,8)(9,10)(12,14)(17,21)(20,22);(4,5)(11,12)(13,14)(15,16,19,18)(17,20,21,22);(3,4,6,5)(7,8,9,10)(11,12)(13,14);(7,8)(9,10)(11,12)(13,14)(15,17)(16,20)(18,22)(19,21);(3,5,6,4)(7,8)(9,10)(11,12)(13,14)(15,18,19,16)(17,22,21,20)

Conjugacy classes & character table

196 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((1,2)(4,5)(8,10)(11,12)(13,14), (7,8)(9,10)(12,14)(17,21)(20,22), (4,5)(11,12)(13,14)(15,16,19,18)(17,20,21,22), (3,4,6,5)(7,8,9,10)(11,12)(13,14), (7,8)(9,10)(11,12)(13,14)(15,17)(16,20)(18,22)(19,21), (3,5,6,4)(7,8)(9,10)(11,12)(13,14)(15,18,19,16)(17,22,21,20));