Finite Group Databasebeta

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C₂×#845309 #72278871

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

Aliases

Subgroups

164199 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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