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C₂×#2771 #52211

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

Aliases

Subgroups

1035 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 45199);