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C₂×#210728 #72285331

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

Aliases

Subgroups

5669 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 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((4,6), (3,4,5,6)(16,19)(17,20)(21,22), (1,2), (7,8,9,11,10,12,13,14)(15,16,17,19,18,21,20,22), (15,16,20,22,18,21,17,19));