Finite Group Databasebeta

← Group #136378

Character table — Group #136378

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222244444444444888888888888888888816161616161616161616161616163232
order12222244444488884444444888844444488888161616161616161644444488881616161688
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111-1-1-1-111111-1-111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1
χ6111111111111111111-1-1-1-111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ7111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111
χ8111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ91111-1-1-11111-111111-111-1-1-1-1-1111-1ii−i−i-111-1-11111-1-1-1-1i−iii−i−iii−i−i11-1-1i−i
χ101111-1-1-11111-111111-111-1-1-1-1-1111-1ii−i−i-111-1-1-1-1-1-11111i−iii−i−i−i−iii-1-111−ii
χ111111-1-1-11111-111111-111-1-1-1-1-1111-1−i−iii-111-1-11111-1-1-1-1−ii−i−iii−i−iii11-1-1−ii
χ121111-1-1-11111-111111-111-1-1-1-1-1111-1−i−iii-111-1-1-1-1-1-11111−ii−i−iiiii−i−i-1-111i−i
χ131111-1-1-11111-111111-1-1-111-1-1-111-11ii−i−i-1-1-1111111-1-1-1-1i−i−i−iiiii−i−i-1-111−ii
χ141111-1-1-11111-111111-1-1-111-1-1-111-11ii−i−i-1-1-111-1-1-1-11111i−i−i−iii−i−iii11-1-1i−i
χ151111-1-1-11111-111111-1-1-111-1-1-111-11−i−iii-1-1-1111111-1-1-1-1−iiii−i−i−i−iii-1-111i−i
χ161111-1-1-11111-111111-1-1-111-1-1-111-11−i−iii-1-1-111-1-1-1-11111−iiii−i−iii−i−i11-1-1−ii
χ17222222222222-2-2-2-22222222-2-2-2-2220000-2-2-2-2-2000000000000000000000000
χ18222222222222-2-2-2-222-2-2-2-22-2-2-2-2-2-20000-22222000000000000000000000000
χ192222222-2-22222222-2-20000-222-2-2002222-2000000000000-2-200000000000000
χ202222222-2-22222222-2-20000-222-2-200-2-2-2-2-20000000000002200000000000000
χ212222222-2-2222-2-2-2-2-2-20000-2-2-2220000002000000000000002-22-20000000000
χ222222222-2-2222-2-2-2-2-2-20000-2-2-222000000200000000000000-22-220000000000
χ23222222-222-2-2-20000-222222-20000-2-2000000000i2i2−i2−i2i2i2−i2−i20000000000i2−i2i2−i200
χ24222222-222-2-2-20000-222222-20000-2-2000000000−i2−i2i2i2−i2−i2i2i20000000000−i2i2−i2i200
χ25222222-222-2-2-20000-22-2-2-2-2-2000022000000000i2i2−i2−i2i2i2−i2−i20000000000−i2i2−i2i200
χ26222222-222-2-2-20000-22-2-2-2-2-2000022000000000−i2−i2i2i2−i2−i2i2i20000000000i2−i2i2−i200
χ272222-2-2222-2-220000-2-222-2-220000-22000000000i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i200
χ282222-2-2222-2-220000-2-222-2-220000-22000000000−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i200
χ292222-2-2222-2-220000-2-2-2-222200002-2000000000i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i200
χ302222-2-2222-2-220000-2-2-2-222200002-2000000000−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i200
χ312222-2-2-22222-2-2-2-2-22-222-2-2-222-2-22-200002-2-222000000000000000000000000
χ322222-2-2-22222-2-2-2-2-22-2-2-222-222-2-2-220000222-2-2000000000000000000000000
χ332222-2-2-2-2-222-22222-2200002-2-2-2-2002i2i−2i−2i2000000000000−2i2i00000000000000
χ342222-2-2-2-2-222-22222-2200002-2-2-2-200−2i−2i2i2i20000000000002i−2i00000000000000
χ352222-2-2-2-2-222-2-2-2-2-2-22000022222000000-2000000000000002i−2i−2i2i0000000000
χ362222-2-2-2-2-222-2-2-2-2-2-22000022222000000-200000000000000−2i2i2i−2i0000000000
χ3722-2-22-2-2002-22-2-22200000002-200002-22-200000i2−i2i2−i2i2−i2i2−i2000000i2−i2i2−i2000000
χ3822-2-22-2-2002-22-2-22200000002-200002-22-200000−i2i2−i2i2−i2i2−i2i2000000−i2i2−i2i2000000
χ3922-2-22-2-2002-22-2-22200000002-20000-22-2200000i2−i2i2−i2i2−i2i2−i2000000−i2i2−i2i2000000
χ4022-2-22-2-2002-22-2-22200000002-20000-22-2200000−i2i2−i2i2−i2i2−i2i2000000i2−i2i2−i2000000
χ4122-2-2-222002-2-2-2-2220000000-2200002i−2i−2i2i00000i2−i2i2−i2−i2i2−i2i2000000−222−2000000
χ4222-2-2-222002-2-2-2-2220000000-2200002i−2i−2i2i00000−i2i2−i2i2i2−i2i2−i20000002−2−22000000
χ4322-2-2-222002-2-2-2-2220000000-220000−2i2i2i−2i00000i2−i2i2−i2−i2i2−i2i20000002−2−22000000
χ4422-2-2-222002-2-2-2-2220000000-220000−2i2i2i−2i00000−i2i2−i2i2i2−i2i2−i2000000−222−2000000
χ45444444-4-4-4-4-4-400004-400004000000000000000000000000000000000000000
χ464444-4-44-4-4-4-440000440000-4000000000000000000000000000000000000000
χ4744-4-44-4400-44-4000000000000000000000000002-2-222-2-220000000000000000
χ4844-4-44-4400-44-400000000000000000000000000-222-2-222-20000000000000000
χ4944-4-44-4-4004-4444-4-40000000-440000000000000000000000000000000000000
χ5044-4-4-444004-4-444-4-400000004-40000000000000000000000000000000000000
χ5144-4-4-44-400-444000000000000000000000000002-2-22-222-20000000000000000
χ5244-4-4-44-400-44400000000000000000000000000-222-22-2-220000000000000000
χ534-44-40004-40002i2−2i22i2−2i200004-40002i2−2i20000000002i2−2i2000000000000000000000000
χ544-44-40004-40002i2−2i22i2−2i20000-440002i2−2i2000000000−2i22i2000000000000000000000000
χ554-44-40004-4000−2i22i2−2i22i200004-4000−2i22i2000000000−2i22i2000000000000000000000000
χ564-44-40004-4000−2i22i2−2i22i20000-44000−2i22i20000000002i2−2i2000000000000000000000000
χ574-44-4000-440002i2−2i22i2−2i2004-400000−2i22i200000002i2−2i200000000000000000000000000
χ584-44-4000-440002i2−2i22i2−2i200-4400000−2i22i20000000−2i22i200000000000000000000000000
χ594-44-4000-44000−2i22i2−2i22i2004-4000002i2−2i20000000−2i22i200000000000000000000000000
χ604-44-4000-44000−2i22i2−2i22i200-44000002i2−2i200000002i2−2i200000000000000000000000000
χ618-8-88000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000
χ628-8-8800000000−4i24i24i2−4i20000000000000000000000000000000000000000000000

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