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C₂×#13361 #498913

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

Aliases

Subgroups

2113 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406109);