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C₂×#7630942 #72307152

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

Aliases

Subgroups

114413 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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