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C₂×#12011 #483338

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

Aliases

Subgroups

516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 390534);