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C₂×#7733246 #72295101

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

Aliases

Subgroups

109953 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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