Finite Group Databasebeta

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C₂×#72218795 #72267183

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

Aliases

Subgroups

2996704 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

344 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((4,6)(8,10)(12,14)(16,18)(20,22), (1,2), (16,18)(20,22), (7,8)(9,10)(19,20)(21,22), (11,12)(13,14)(15,16)(17,18)(19,20)(21,22), (3,4)(5,6)(7,8)(9,10)(11,12)(13,14));