Finite Group Databasebeta

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C₂×#72215608 #72323770

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

Aliases

Subgroups

At least 6992 conjugacy classes of subgroups; only the 47880 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

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