Finite Group Databasebeta

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C₂×#72298087 #72299622

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

Aliases

Subgroups

At least 12564 conjugacy classes of subgroups; only the 67464 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

452 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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