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C₂×#13638 #512723

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

Aliases

Subgroups

420 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 419919);