Finite Group Databasebeta

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C₂×#72214353 #72234777

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

Aliases

Subgroups

At least 6349 conjugacy classes of subgroups; only the 4768 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

224 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), (8,12)(9,15)(10,17)(13,18)(14,21)(19,20), (8,13)(12,18), (3,4)(5,6)(7,8,9,14,11,13,15,20)(10,12,16,19,17,18,22,21), (4,6));