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C₂×#1905 #20997

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

Aliases

Subgroups

839 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4,8,12,9,14,7,13)(5,15,18,25,19,28,17,10)(6,20,22,11,23,26,21,27)(16,24,31,33,32,34,30,29);(3,5)(4,10,14,25)(6,16)(7,17)(8,18)(9,19)(11,24,27,34)(12,15,13,28)(20,29,26,33)(21,30)(22,31)(23,32);(3,6,9,23)(4,11,14,27)(5,16,19,32)(7,22,8,21)(10,24,25,34)(12,20,13,26)(15,29,28,33)(17,31,18,30)

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 13985);