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C₂×#3269 #61027

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

Aliases

Subgroups

1387 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54015);