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C₂×#2931 #60135

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

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, 53123);