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C₂×#688038 #72299472

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

Aliases

Subgroups

61337 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

184 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)(7,8,9,10)(12,14)(15,16,20,21)(17,22,18,19), (7,8)(9,10)(12,14)(16,21)(17,18), (3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,17,20,18)(16,19,21,22), (3,4)(5,6)(7,8)(9,10)(15,18,20,17)(16,19,21,22), (3,4)(5,6)(7,8)(9,10)(15,19)(16,17)(18,21)(20,22), (1,2));