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C₂×C₄×#135 #60151

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

Aliases

Subgroups

1447 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53139);