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C₂×#7684164 #72304286

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

Aliases

Subgroups

86837 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

226 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)(3,4)(5,6)(7,8,12,10)(9,13,14,11), (3,4)(5,6)(7,9)(8,13)(10,11)(12,14)(15,16)(17,20)(18,21)(19,22), (3,4)(5,6)(7,9)(8,13)(10,11)(12,14)(15,17)(16,19)(18,22)(20,21), (3,4)(5,6)(7,10,12,8)(9,11,14,13), (3,4,5,6)(7,9)(8,13)(10,11)(12,14)(15,17)(16,20)(18,22)(19,21), (3,4)(5,6)(7,11,12,13)(8,14,10,9), (7,9)(8,13)(10,11)(12,14)(15,16)(17,19)(18,21)(20,22));