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C₂×#1710 #19598

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

Aliases

Subgroups

375 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 12586);