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C₂×#1418629 #72299192

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

Aliases

Subgroups

50485 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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