Finite Group Databasebeta

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C₂×#525184 #72323920

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

Aliases

Subgroups

49705 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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)(11,12,14,13)(16,19)(17,21), (8,10)(15,16)(17,22)(18,19)(20,21), (7,8)(9,10)(11,13,14,12)(17,21)(20,22), (3,4)(5,6)(15,16)(17,20)(18,19)(21,22), (1,2), (3,4)(5,6)(15,17,18,21)(16,20,19,22));