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C₂×#13466 #499301

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

Aliases

Subgroups

778 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,11,16)(5,17)(6,23)(7,14,28,34)(8,13,9,31)(10,18,30,15)(12,25)(19,27)(20,33)(21,24)(22,32)(26,29);(3,5,7,19,10,21,8,29,11,22,28,23,30,12,9,20)(4,6,13,17,15,26,14,25,16,27,31,32,18,33,34,24);(3,6)(4,12)(5,18)(7,25)(8,17)(9,32)(10,33)(11,27)(13,19)(14,20)(15,22)(16,21)(23,31)(24,28)(26,30)(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, 406497);