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C₂×#648037 #72334512

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

Aliases

Subgroups

74017 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)(16,17)(20,21);(4,6)(7,8,9,10)(11,12)(13,14)(16,17)(18,22);(4,6)(8,10)(12,14)(15,16,19,17)(18,21,22,20);(4,6)(8,10)(11,12)(13,14)(15,17,19,16)(18,20,22,21);(1,2);(3,4)(5,6)(7,8)(9,10)(15,18)(16,20)(17,21)(19,22)

Conjugacy classes & character table

208 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)(16,17)(20,21), (4,6)(7,8,9,10)(11,12)(13,14)(16,17)(18,22), (4,6)(8,10)(12,14)(15,16,19,17)(18,21,22,20), (4,6)(8,10)(11,12)(13,14)(15,17,19,16)(18,20,22,21), (1,2), (3,4)(5,6)(7,8)(9,10)(15,18)(16,20)(17,21)(19,22));