Finite Group Databasebeta

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C₂×#652786 #72298714

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

Aliases

Subgroups

76185 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 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((12,14)(16,19)(20,21), (4,6)(8,10)(11,12)(13,14)(15,16)(17,21)(18,19)(20,22), (3,4,5,6)(7,8,9,10)(16,19)(17,22), (7,8)(9,10)(15,16)(17,20)(18,19)(21,22), (3,4)(5,6)(7,8)(9,10)(15,17)(16,20)(18,22)(19,21), (1,2));