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C₂×#2836 #36659

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

Aliases

Subgroups

925 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 29647);