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C₂×#13123 #494832

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

Aliases

Subgroups

774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 402028);