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C₂×#2757 #52194

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

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, 45182);