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C₂×#7630941 #72307162

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

Aliases

Subgroups

107445 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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