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C₂×#13054 #494608

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

Aliases

Subgroups

1913 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)(16,29)(17,26)(18,31,21,34)(20,28)(23,30)(25,32,27,33);(3,5,15,17,8,16,6,19)(4,9,24,14,13,26,11,29)(7,21,23,33,22,18,20,32)(10,27,28,34,12,25,30,31);(4,10)(5,16)(7,22)(9,25)(11,30)(12,13)(14,31)(17,19)(20,23)(24,28)(26,27)(29,34)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401804);