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C₂×#2080 #23648

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

Aliases

Subgroups

453 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 16636);