Finite Group Databasebeta

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C₂×#7798105 #72298428

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

Aliases

Subgroups

At least 6928 conjugacy classes of subgroups; only the 31901 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

196 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((4,6)(7,8)(9,13)(10,12)(11,14)(16,19)(20,22), (3,4)(5,6)(7,9)(8,13)(10,11)(12,14)(16,19)(17,21), (8,10)(11,13)(16,19)(20,22), (7,8,12,10)(9,11,14,13)(15,16,18,19)(17,22,21,20), (7,10,12,8)(9,11,14,13)(15,17)(16,20)(18,21)(19,22), (7,11)(8,9)(10,14)(12,13)(15,17)(16,20)(18,21)(19,22), (1,2));