Finite Group Databasebeta

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C₂×#625761 #72331925

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

Aliases

Subgroups

65641 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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