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C₂×#12027 #483411

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

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, 390607);