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C₂×#2781 #52222

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

Aliases

Subgroups

1165 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 45210);