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C₂×#13434 #499147

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

Aliases

Subgroups

1125 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406343);