Finite Group Databasebeta

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C₂×#72233119 #72237494

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

Aliases

Subgroups

At least 9960 conjugacy classes of subgroups; only the 5168 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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