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C₂×#13459 #499209

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

Aliases

Subgroups

810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406405);