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C₂×#33470 #7622633

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

Aliases

Subgroups

1878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 66 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529829);