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C₂×#7630950 #72256248

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

Aliases

Subgroups

114133 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 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((15,16)(17,21)(18,20)(19,22), (15,16,18,20)(17,19,22,21), (4,6), (1,2), (8,11)(12,13), (3,4,5,6)(7,8)(9,13)(10,11)(12,14)(15,16)(17,19)(18,20)(21,22), (7,9,10,14)(8,12,11,13)(15,17)(16,19)(18,22)(20,21));