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C₂×#12068 #483598

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

Aliases

Subgroups

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 390794);