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C₂×#1393170 #72298651

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

Aliases

Subgroups

77097 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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