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C₂×#13173 #495040

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

Aliases

Subgroups

620 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 402236);