Finite Group Databasebeta

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C₂×#72303265 #72341852

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

Aliases

Subgroups

At least 9904 conjugacy classes of subgroups; only the 43624 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

392 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((1,2)(8,10)(12,14)(15,16,19,18)(17,20,22,21), (4,6)(7,8,9,10)(11,12,13,14)(15,17)(16,20)(18,21)(19,22), (8,10)(11,12,13,14), (7,8,9,10)(11,12,13,14)(15,18,19,16)(17,21,22,20), (7,8,9,10)(11,12,13,14)(15,17)(16,20)(18,21)(19,22), (7,8)(9,10)(11,12)(13,14), (3,4,5,6)(15,16,19,18)(17,21,22,20));