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C₂×#515835 #72331167

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

Aliases

Subgroups

70105 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

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