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C₂×C₄×Q₁₆ #2938

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

Aliases

Subgroups

244 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 1670);