Finite Group Databasebeta

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C₂×#7692752 #72298840

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

Aliases

Subgroups

At least 6736 conjugacy classes of subgroups; only the 32405 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

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