Finite Group Databasebeta

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C₂×#2806025 #72296321

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

Aliases

Subgroups

45349 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

160 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((4,6)(7,8)(9,10)(12,14)(16,20)(17,22), (3,4)(5,6)(7,8,10,9)(11,12)(13,14)(15,16,19,20)(17,18,22,21), (3,4,5,6)(7,8,10,9)(17,22)(18,21), (8,9)(15,17)(16,21)(18,20)(19,22), (3,4)(5,6)(7,9,10,8)(15,18,19,21)(16,17,20,22), (1,2));