Finite Group Databasebeta

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C₂×#1082725 #72325043

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

Aliases

Subgroups

65611 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

172 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((3,4)(5,6)(7,8,10,9)(16,19)(20,22), (8,9)(11,12,14,13)(15,16,18,19)(17,20,21,22), (12,13)(16,19)(17,21), (4,6)(8,9)(15,16)(17,20)(18,19)(21,22), (1,2), (3,4)(5,6)(7,9,10,8)(11,13,14,12)(15,17,18,21)(16,20,19,22));