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C₂×#2814077 #72295052

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

Aliases

Subgroups

53539 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

160 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)(8,9)(12,14)(15,16)(17,20)(18,19)(21,22), (3,4,5,6)(7,8,10,9)(12,14)(17,21)(20,22), (3,4)(5,6)(7,8,10,9)(11,12,13,14)(16,19)(17,21), (7,9,10,8)(15,16)(17,20)(18,19)(21,22), (3,4)(5,6)(15,17)(16,20)(18,21)(19,22), (1,2));