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C₂×#7631310 #72304183

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

Aliases

Subgroups

115177 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

244 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((1,2)(4,6)(15,16,19,17)(18,21,22,20), (7,8)(9,12)(10,13)(11,14), (7,9)(8,11)(10,14)(12,13), (4,6)(15,17,19,16)(18,20,22,21), (3,4,5,6)(7,9)(8,12)(10,14)(11,13)(15,18,19,22)(16,20,17,21), (15,17)(16,19)(18,20)(21,22), (7,8)(9,11)(10,13)(12,14));