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C₂×#12026 #483410

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

Aliases

Subgroups

408 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 66 points:

(1,2);(3,4,8,15,10,16,33,45,11,17,32,14,9,36,7,31)(5,18,21,38,23,47,20,39,24,43,34,60,22,56,54,12)(6,25,27,58,29,42,26,44,30,59,35,61,28,13,40,41)(19,48,50,37,52,62,64,57,53,66,55,63,51,46,49,65);(3,5,7,20,9,22,32,21,11,24,33,54,10,23,8,34)(4,12,14,18,16,38,31,47,17,39,15,43,36,60,45,56)(6,19,26,49,28,51,27,55,30,53,40,64,29,52,35,50)(13,37,41,46,25,57,58,48,42,63,44,62,59,65,61,66);(3,6,9,28,11,30,10,29)(4,13,16,25,17,42,36,59)(5,19,22,51,24,53,23,52)(7,26,32,27,33,40,8,35)(12,37,38,57,39,63,60,65)(14,41,31,58,15,44,45,61)(18,46,47,48,43,62,56,66)(20,49,21,55,54,64,34,50)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 390606);