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C₂×#2480 #34660

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

Aliases

Subgroups

2051 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27648);