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C₂×#2528 #34792

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

Aliases

Subgroups

939 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 27780);