Finite Group Databasebeta

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C₂×#612509 #72298673

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

Aliases

Subgroups

73693 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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((3,4,5,6)(8,10)(12,14)(16,20)(18,21), (3,4,5,6)(8,10)(11,12)(13,14)(15,16)(17,21)(18,22)(19,20), (4,6)(7,8,9,10)(16,20)(18,21), (3,4,5,6)(7,8,9,10)(15,17,19,22)(16,18,20,21), (3,4)(5,6)(7,8)(9,10)(15,18)(16,17)(19,21)(20,22), (1,2));