Finite Group Databasebeta

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C₂×#496124 #72224813

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

Aliases

Subgroups

5191 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

136 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((7,8,9,12,10,13,15,20,11,14,16,19,17,21,22,18), (4,6)(8,12,14,19)(9,15)(10,17)(13,18,21,20)(16,22), (8,13,14,21)(9,16)(12,18,19,20)(15,22), (1,2)(8,14)(12,19)(13,21)(18,20), (3,4,5,6));