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C₂×#4122182 #72297398

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

Aliases

Subgroups

44195 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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