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C₂×#2777 #52217

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

Aliases

Subgroups

981 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 45205);