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C₂×#2735 #52170

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

Aliases

Subgroups

1659 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(3,4,6,7)(5,8,9,10)(11,12,14,16)(13,17,18,15)(19,20,23,24)(21,25,26,22);(4,7)(5,9)(11,12,14,16)(13,15,18,17)(19,21,23,26)(20,22,24,25);(3,5)(4,8)(6,9)(7,10)(11,12)(13,15)(14,16)(17,18)(19,21)(20,22)(23,26)(24,25);(3,4)(5,8)(6,7)(9,10)(11,13)(12,15)(14,18)(16,17)(19,22)(20,21)(23,25)(24,26)

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 45158);