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C₂×#7670206 #72240946

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

Aliases

Subgroups

202789 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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((7,8)(9,12)(10,13)(11,14)(15,16)(17,18)(19,21)(20,22), (4,6)(7,9)(8,11)(10,14)(12,13)(15,17)(16,20)(18,21)(19,22), (4,6), (16,21)(18,20), (7,9)(8,12)(10,14)(11,13)(15,17)(16,18)(19,22)(20,21), (1,2), (3,4)(5,6)(7,8)(9,11)(10,13)(12,14)(15,18)(16,22)(17,21)(19,20));