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C₂×#13053 #494607

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

Aliases

Subgroups

1891 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)(6,11,15,24)(7,12)(9,19)(10,22)(16,27)(17,32,21,31)(18,29)(20,28)(23,30)(25,34,26,33);(3,5,15,16,8,18,6,19)(4,9,24,14,13,27,11,29)(7,21,23,34,22,17,20,33)(10,25,28,31,12,26,30,32);(4,10)(7,22)(9,25)(11,30)(12,13)(14,31)(17,21)(20,23)(24,28)(26,27)(29,32)(33,34)

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401803);