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C₂×#3309 #61137

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

Aliases

Subgroups

1121 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54125);