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C₂×#2790 #52234

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

Aliases

Subgroups

1079 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)(13,17)(14,15)(16,18)(19,20,22,24)(21,25,26,23);(4,7)(8,10)(12,15)(13,18)(19,20)(21,25)(22,24)(23,26);(3,4,6,7)(5,8,9,10)(11,12)(13,16)(14,15)(17,18);(3,5,6,9)(4,8,7,10)(11,13,14,18)(12,16,15,17)(19,21,22,26)(20,23,24,25)

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, 45222);