Finite Group Databasebeta

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C₂×#72278047 #72297073

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

Aliases

Subgroups

At least 22016 conjugacy classes of subgroups; only the 10744 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

308 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((8,10)(12,14), (4,6)(8,10)(11,12)(13,14)(16,18)(19,20)(21,22), (8,10)(12,14)(15,16)(17,18)(19,20,21,22), (4,6)(8,10)(16,18), (3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22), (1,2));