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C₂×#13625 #512701

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

Aliases

Subgroups

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 419897);