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C₂×#33658 #7623060

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

Aliases

Subgroups

1550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530256);