Finite Group Databasebeta

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C₂×#72251015 #72289569

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

Aliases

Subgroups

At least 6764 conjugacy classes of subgroups; only the 26232 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

416 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((20,22), (7,8)(9,10)(16,18), (15,16)(17,18)(19,20,21,22), (1,2), (4,6)(8,10)(11,12,13,14)(15,16)(17,18), (3,4)(5,6)(7,8)(9,10)(11,12)(13,14));