Finite Group Databasebeta

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C₂×#6342373 #72296215

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

Aliases

Subgroups

423029 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

304 conjugacy classes. The character table is too large to display.

Relationships

GAP

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

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