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C₂×#3273 #61032

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

Aliases

Subgroups

1521 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 54020);