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C₂×#7642896 #72334333

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

Aliases

Subgroups

114717 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 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)(10,11)(13,14)(16,19)(20,22), (3,4,5,6)(7,8)(9,13)(10,11)(12,14)(17,21)(20,22), (3,4)(5,6)(8,11)(9,14)(15,16)(17,22)(18,19)(20,21), (3,4)(5,6)(7,8)(9,13)(10,11)(12,14)(15,16)(17,22)(18,19)(20,21), (1,2), (7,9)(8,12)(10,14)(11,13)(15,17)(16,20)(18,21)(19,22), (7,9)(8,12)(10,14)(11,13));