Finite Group Databasebeta

← Group #351623

Character table — Group #351623

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444444444888888888888888888888888161616161616161632323232
order12222222444444444488888888244444444444888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-111-1-111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-111-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ9111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ10111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ11111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-111-1-1-11-11
χ12111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-111-1-1111-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-11111-1-1-1-1111111-1-1-1-1111-1-11
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-11111-1-1-1-11111-1-11111-1-1-111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-111111111-1-1-1-111-1-1-1-111-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-111111111-1-1-1-1-1-11111-1-11-1-11
χ172222222222-2-2-2-222-2-20000000022-222-2-2-2-222-2000000000000000000000000
χ182222222222-2-2-2-222-2-20000000022-2-2-22222-2-2-2000000000000000000000000
χ192222222222-2-2-2-222-2-200000000-2-222222-2-2-2-22000000000000000000000000
χ202222222222-2-2-2-222-2-200000000-2-22-2-2-2-222222000000000000000000000000
χ2122222222-2-22222-2-2-2-22222-2-2-2-22-2-200000000222-2-200000000000000000000
χ2222222222-2-22222-2-2-2-22222-2-2-2-2-22200000000-2-2-22200000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-222222-2-2000000002-2-22200000000000000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-22222-22200000000-222-2-200000000000000000000
χ2522222222-2-2-2-2-2-2-2-222000000002-2200000000-200002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-222000000002-2200000000-20000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-22200000000-22-200000000200002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-22200000000-22-20000000020000−2i−2i2i2i2i2i−2i−2i000000000000
χ292-222-2-2-222-222-2-22-22-200000000000002i−2i002i−2i02i−2i2i−2i2-22-20000000000000000
χ302-222-2-2-222-222-2-22-22-200000000000002i−2i002i−2i0−2i2i−2i2i-22-220000000000000000
χ312-222-2-2-222-222-2-22-22-20000000000000−2i2i00−2i2i02i−2i2i−2i-22-220000000000000000
χ322-222-2-2-222-222-2-22-22-20000000000000−2i2i00−2i2i0−2i2i−2i2i2-22-20000000000000000
χ332-222-2-2-222-2-2-2222-2-2222-2-222-2-2000002i−2i00−2i2i0000000002i−2i2i−2i000000000000
χ342-222-2-2-222-2-2-2222-2-2222-2-222-2-200000−2i2i002i−2i000000000−2i2i−2i2i000000000000
χ352-222-2-2-222-2-2-2222-2-22-2-222-2-222000002i−2i00−2i2i000000000−2i2i−2i2i000000000000
χ362-222-2-2-222-2-2-2222-2-22-2-222-2-22200000−2i2i002i−2i0000000002i−2i2i−2i000000000000
χ372-222-2-2-22-2222-2-2-22-22000000000002i−2i002i−2i0002i−2i−2i2i00002-2-22000000000000
χ382-222-2-2-22-2222-2-2-22-22000000000002i−2i002i−2i000−2i2i2i−2i0000-222-2000000000000
χ392-222-2-2-22-2222-2-2-22-2200000000000−2i2i00−2i2i0002i−2i−2i2i0000-222-2000000000000
χ402-222-2-2-22-2222-2-2-22-2200000000000−2i2i00−2i2i000−2i2i2i−2i00002-2-22000000000000
χ412-222-2-2-22-22-2-222-222-222-2-2-2-2220002i−2i00−2i2i0000000−2i2i2i−2i0000000000000000
χ422-222-2-2-22-22-2-222-222-222-2-2-2-222000−2i2i002i−2i00000002i−2i−2i2i0000000000000000
χ432-222-2-2-22-22-2-222-222-2-2-22222-2-20002i−2i00−2i2i00000002i−2i−2i2i0000000000000000
χ442-222-2-2-22-22-2-222-222-2-2-22222-2-2000−2i2i002i−2i0000000−2i2i2i−2i0000000000000000
χ45444-44-4-4-44-40000-440022−2222−2222−2222−22000000000000000000000000000000000000
χ46444-44-4-4-44-40000-4400−2222−2222−2222−2222000000000000000000000000000000000000
χ47444-44-4-4-4-4400004-40022−2222−22−2222−2222000000000000000000000000000000000000
χ48444-44-4-4-4-4400004-400−2222−222222−2222−22000000000000000000000000000000000000
χ4944-4-4-44-44004-44-40000000000000000000000000000000000002i2−2i20000000000
χ5044-4-4-44-44004-44-4000000000000000000000000000000000000−2i22i20000000000
χ5144-4-4-44-4400-44-4400000000000000000000000000000000000000002i2−2i2000000
χ5244-4-4-44-4400-44-440000000000000000000000000000000000000000−2i22i2000000
χ534-44-4-444-4440000-4-40022−22−222222−22−2222000000000000000000000000000000000000
χ544-44-4-444-4440000-4-400−222222−22−222222−22000000000000000000000000000000000000
χ554-44-4-444-4-4-40000440022−22−2222−222222−22000000000000000000000000000000000000
χ564-44-4-444-4-4-400004400−222222−2222−22−2222000000000000000000000000000000000000
χ574-4-4-44-444004-4-4400000000000000000000000000000000000000000022−220000
χ584-4-4-44-444004-4-44000000000000000000000000000000000000000000−22220000
χ594-4-4-44-44400-444-40000000000000000000000000000000000000022−2200000000
χ604-4-4-44-44400-444-400000000000000000000000000000000000000−222200000000
χ6188-88-8-88-8000000000000000000000000000000000000000000000000000000
χ628-8-8888-8-8000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).