Finite Group Databasebeta

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C₂×#7966826 #72323776

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

Aliases

Subgroups

At least 6928 conjugacy classes of subgroups; only the 31997 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)(16,20)(18,22);(7,9)(8,10)(11,12)(13,14);(7,10)(8,12)(9,14)(11,13)(15,16,19,20)(17,18,21,22);(3,4)(5,6);(1,2);(3,4)(5,6)(7,10)(8,9)(11,13)(12,14)(15,17)(16,18)(19,21)(20,22);(7,9)(8,13)(10,14)(11,12)(15,18)(16,21)(17,20)(19,22)

Conjugacy classes & character table

202 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)(16,20)(18,22), (7,9)(8,10)(11,12)(13,14), (7,10)(8,12)(9,14)(11,13)(15,16,19,20)(17,18,21,22), (3,4)(5,6), (1,2), (3,4)(5,6)(7,10)(8,9)(11,13)(12,14)(15,17)(16,18)(19,21)(20,22), (7,9)(8,13)(10,14)(11,12)(15,18)(16,21)(17,20)(19,22));