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C₂×#2498 #34805

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

Aliases

Subgroups

1557 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(8,9)(10,14)(15,16,19,21)(17,18,22,20);(7,8,11,9)(10,12,14,13)(15,17,19,22)(16,20,21,18);(3,4,5,6)(7,9,11,8)(10,13,14,12)(15,17)(16,18)(19,22)(20,21);(7,10)(8,12)(9,13)(11,14)(15,18)(16,17)(19,20)(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, 27793);