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C₂×#7646027 #72302529

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

Aliases

Subgroups

114945 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 22 points:

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

Conjugacy classes & character table

196 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((9,13)(12,14)(15,16)(17,19)(18,20)(21,22), (4,6)(8,11)(12,14)(15,16,18,20)(17,19,22,21), (3,4)(5,6)(15,16)(17,21)(18,20)(19,22), (15,17)(16,19)(18,22)(20,21), (7,8)(9,12)(10,11)(13,14), (1,2), (7,9,10,13)(8,12,11,14));