Finite Group Databasebeta

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C₂×#617353 #72286848

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

Aliases

Subgroups

163873 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

184 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)(8,10)(12,14), (8,10)(16,19)(20,21), (11,12,13,14)(15,16)(17,20)(18,19)(21,22), (1,2), (3,4)(5,6)(7,8)(9,10)(15,16)(17,21)(18,19)(20,22), (15,17)(16,20)(18,22)(19,21));