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C₂×#2587 #34836

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

Aliases

Subgroups

1135 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27824);