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C₂×#419 #2894

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

Aliases

Subgroups

376 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)(9,16)(10,14)(11,20)(12,15)(13,18)(17,21)(19,22);(7,9,12,19)(8,13,15,21)(10,18,11,17)(14,22,20,16);(7,10,12,11)(8,14,15,20)(9,17,19,18)(13,16,21,22)

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 1626);