Finite Group Databasebeta

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C₂×#7659296 #72298859

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

Aliases

Subgroups

103653 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 22 points:

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

Conjugacy classes & character table

196 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((9,14)(11,12)(16,19)(20,21), (4,6)(7,8)(9,12)(10,13)(11,14)(15,16)(17,20)(18,19)(21,22), (3,4,5,6)(15,16)(17,21)(18,19)(20,22), (7,9,10,14)(8,11,13,12)(15,16,18,19)(17,21,22,20), (7,9)(8,12)(10,14)(11,13)(15,16)(17,20)(18,19)(21,22), (7,8)(9,12)(10,13)(11,14)(15,17)(16,20)(18,22)(19,21), (1,2));