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C₂×#648387 #72286799

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

Aliases

Subgroups

163413 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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