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C₂×#7670220 #72256223

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

Aliases

Subgroups

114339 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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((7,8,10,12)(9,11,13,14)(16,19)(20,22), (15,16,18,19)(17,20,21,22), (4,6), (1,2), (9,13)(11,14)(17,21)(20,22), (3,4,5,6)(7,9)(8,11)(10,13)(12,14)(15,17)(16,20)(18,21)(19,22), (7,8)(9,11)(10,12)(13,14)(15,16)(17,20)(18,19)(21,22));