Finite Group Databasebeta

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C₂×#613321 #72313572

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

Aliases

Subgroups

249277 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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