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C₂×#7899241 #72331495

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

Aliases

Subgroups

86229 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

190 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)(9,12)(10,11)(13,14), (3,4)(5,6)(8,10)(12,13)(15,16)(17,18)(19,21)(20,22), (7,9)(8,12)(10,13)(11,14)(15,17)(16,20)(18,21)(19,22), (4,5)(7,9,11,14)(8,12,10,13)(15,16)(17,18)(19,21)(20,22), (1,2), (7,9)(8,12)(10,13)(11,14)(15,16)(17,20)(18,22)(19,21), (3,5,6,4)(7,10,11,8)(9,13,14,12)(15,18,19,20)(16,17,21,22));