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C₂×#3485 #62774

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

Aliases

Subgroups

5843 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55762);