Finite Group Databasebeta

← Group #136359

Character table — Group #136359

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122224444444444448888888888888888888888881616161616161616161616163232
order122222224444444488888888444444441616161616161616161616161616161622444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1
χ9111-1-1-11-1-111-1-11-1111-1-1-111-1ii−i−i11-1-11111-1-1-1-1iiii−i−i−i−i1-1i−ii−ii−i11-1-1i−i
χ10111-1-1-11-1-111-1-11-1111-1-1-111-1ii−i−i11-1-1-1-1-1-11111−i−i−i−iiiii1-1i−ii−ii−i-1-111−ii
χ11111-1-1-11-1-111-1-11-1111-1-1-111-1ii−i−i-1-1111111-1-1-1-1iiii−i−i−i−i-11−ii−iii−i-1-111−ii
χ12111-1-1-11-1-111-1-11-1111-1-1-111-1ii−i−i-1-111-1-1-1-11111−i−i−i−iiiii-11−ii−iii−i11-1-1i−i
χ13111-1-1-11-1-111-1-11-1111-1-1-111-1−i−iii11-1-11111-1-1-1-1−i−i−i−iiiii1-1−ii−ii−ii11-1-1−ii
χ14111-1-1-11-1-111-1-11-1111-1-1-111-1−i−iii11-1-1-1-1-1-11111iiii−i−i−i−i1-1−ii−ii−ii-1-111i−i
χ15111-1-1-11-1-111-1-11-1111-1-1-111-1−i−iii-1-1111111-1-1-1-1−i−i−i−iiiii-11i−ii−i−ii-1-111i−i
χ16111-1-1-11-1-111-1-11-1111-1-1-111-1−i−iii-1-111-1-1-1-11111iiii−i−i−i−i-11i−ii−i−ii11-1-1−ii
χ172222222222222222-2-2-2-2-2-2-2-2222200000000000000000000000000-2-2000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000022000000
χ19222222222222-2-2-2-2222-2-2-2-22000022220000000000000000-2-2000000000000
χ20222222222222-2-2-2-2222-2-2-2-220000-2-2-2-2000000000000000022000000000000
χ21222222222222-2-2-2-2-2-2-22222-20000000000000000000000000022-2-200000000
χ22222222222222-2-2-2-2-2-2-22222-200000000000000000000000000-2-22200000000
χ2322222222-2-2-2-22-2-22000000002-22-2000022−2−222−2−222−2−222−2−200000000000000
χ2422222222-2-2-2-22-2-22000000002-22-20000−2−222−2−222−2−222−2−22200000000000000
χ2522222222-2-2-2-22-2-2200000000-22-22000022−2−222−2−2−2−222−2−22200000000000000
χ2622222222-2-2-2-22-2-2200000000-22-220000−2−222−2−22222−2−222−2−200000000000000
χ27222-2-2-22-22-2-22-2-222000000002i−2i−2i2i000022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000
χ28222-2-2-22-22-2-22-2-222000000002i−2i−2i2i0000−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000
χ29222-2-2-22-22-2-22-2-22200000000−2i2i2i−2i000022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000
χ30222-2-2-22-22-2-22-2-22200000000−2i2i2i−2i0000−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000
χ31222-2-2-22-2-222-22-22-222-222-2-2-2000022-2-20000000000000000-22000000000000
χ32222-2-2-22-2-222-22-22-222-222-2-2-20000-2-22200000000000000002-2000000000000
χ33222-2-2-22-2-222-22-22-2-2-22-2-2222000000000000000000000000002i−2i−2i2i00000000
χ34222-2-2-22-2-222-22-22-2-2-22-2-222200000000000000000000000000−2i2i2i−2i00000000
χ35222-2-2-22-2-222-2-22-22-2-2222-2-222i2i−2i−2i00000000000000000000000000−2i2i000000
χ36222-2-2-22-2-222-2-22-22-2-2222-2-22−2i−2i2i2i000000000000000000000000002i−2i000000
χ3722-222-2-2-2-22-2200002-2-20000200002i−2i2i−2i2−22−22−22−20000000000000000i2−i2i2−i200
χ3822-222-2-2-2-22-2200002-2-20000200002i−2i2i−2i−22−22−22−220000000000000000−i2i2−i2i200
χ3922-222-2-2-2-22-2200002-2-2000020000−2i2i−2i2i2−22−22−22−20000000000000000−i2i2−i2i200
χ4022-222-2-2-2-22-2200002-2-2000020000−2i2i−2i2i−22−22−22−220000000000000000i2−i2i2−i200
χ4122-2-2-22-2222-2-200002-220000-200002i−2i−2i2i2−22−2−22−220000000000000000i2−i2−i2i200
χ4222-2-2-22-2222-2-200002-220000-200002i−2i−2i2i−22−222−22−20000000000000000−i2i2i2−i200
χ4322-2-2-22-2222-2-200002-220000-20000−2i2i2i−2i2−22−2−22−220000000000000000−i2i2i2−i200
χ4422-2-2-22-2222-2-200002-220000-20000−2i2i2i−2i−22−222−22−20000000000000000i2−i2−i2i200
χ4544444444-4-4-4-4-444-40000000000000000000000000000000000000000000000
χ46444-4-4-44-44-4-4444-4-40000000000000000000000000000000000000000000000
χ4744-444-4-4-44-44-4000000000000000000002-2-222-2-220000000000000000000000
χ4844-444-4-4-44-44-400000000000000000000-222-2-222-20000000000000000000000
χ4944-444-4-4-4-44-440000-4440000-400000000000000000000000000000000000000
χ5044-4-4-44-4444-4-40000-44-40000400000000000000000000000000000000000000
χ5144-4-4-44-44-4-444000000000000000000002-2-22-222-20000000000000000000000
χ5244-4-4-44-44-4-44400000000000000000000-222-22-2-220000000000000000000000
χ534-4-44-444-40000000000022−2222−2200000000000000000ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ700000000000000
χ544-4-44-444-40000000000022−2222−2200000000000000000−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ700000000000000
χ554-4-44-444-400000000000−2222−222200000000000000000ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ700000000000000
χ564-4-44-444-400000000000−2222−222200000000000000000−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ700000000000000
χ574-4-4-44-4440000000000022−22−222200000000000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ700000000000000
χ584-4-4-44-4440000000000022−22−222200000000000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ700000000000000
χ594-4-4-44-44400000000000−222222−2200000000000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ700000000000000
χ604-4-4-44-44400000000000−222222−2200000000000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ700000000000000
χ618-888-8-8-88000000000000000000000000000000000000000000000000000000
χ628-88-888-8-8000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.