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C₂×#2741 #52176

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

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, 45164);