Finite Group Databasebeta

← Group #106940

Character table — Group #106940

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222444444444444448888888888888888888888888888888888888888888816161616
order12222222222244444444444422224444444444224444444444444444444444444488888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-111111-1-1-1-11-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-111111-1-1-1-11-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ911111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i
χ1011111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−iii
χ1111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii
χ1211111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i
χ1311111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1111111-11111-1-1-1-111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i
χ1411111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1111111-11111-1-1-1-111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−iii
χ1511111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1111111-111-1-111-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iii
χ1611111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1111111-111-1-111-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iii−i−i
χ17111-1-11-1-111-1-111-1-1-1-1-1-1111111-1-11-111-111-1-1-11-1i−ii−i1-1i−ii−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i1-11-1
χ18111-1-11-1-111-1-111-1-1-1-1-1-1111111-1-11-111-111-1-1-11-1i−ii−i1-1i−ii−iii−i−iii−i−i−i−iii−i−iii-1-111-1-111−i−iii−i−iii-11-11
χ19111-1-11-1-111-1-111-1-1-1-1-1-1111111-1-11-111-111-1-1-11-1−ii−ii1-1−ii−ii−i−iii−i−iiiii−i−iii−i−i-1-111-1-111ii−i−iii−i−i-11-11
χ20111-1-11-1-111-1-111-1-1-1-1-1-1111111-1-11-111-111-1-1-11-1−ii−ii1-1−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii1-11-1
χ21111-1-11-1-111-1-111-1-1-1-1-1-11111-1-1111-111-1-1-111-1-11i−ii−i-11i−ii−i−i−iii−i−iiiii−i−iii−i−i-1-111-1-111−i−iii−i−iii1-11-1
χ22111-1-11-1-111-1-111-1-1-1-1-1-11111-1-1111-111-1-1-111-1-11i−ii−i-11i−ii−i−i−iii−i−iii−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i-11-11
χ23111-1-11-1-111-1-111-1-1-1-1-1-11111-1-1111-111-1-1-111-1-11−ii−ii-11−ii−iiii−i−iii−i−iii−i−iii−i−i11-1-111-1-1−i−iii−i−iii-11-11
χ24111-1-11-1-111-1-111-1-1-1-1-1-11111-1-1111-111-1-1-111-1-11−ii−ii-11−ii−iiii−i−iii−i−i−i−iii−i−iii-1-111-1-111ii−i−iii−i−i1-11-1
χ25111-1-11-1-1-1-11111-1-11111-1-1-1-111-1-11-1-11-1-1-1111-11i−i−ii1-1i−i−iiii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i11-1-1-1-111−iii−i
χ26111-1-11-1-1-1-11111-1-11111-1-1-1-111-1-11-1-11-1-1-1111-11i−i−ii1-1i−i−iiii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii-1-11111-1-1i−i−ii
χ27111-1-11-1-1-1-11111-1-11111-1-1-1-111-1-11-1-11-1-1-1111-11−iii−i1-1−iii−i−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii11-1-1-1-111i−i−ii
χ28111-1-11-1-1-1-11111-1-11111-1-1-1-111-1-11-1-11-1-1-1111-11−iii−i1-1−iii−i−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i-1-11111-1-1−iii−i
χ29111-1-11-1-1-1-11111-1-11111-1-1-1-1-1-1111-1-11-111-1-111-1i−i−ii-11i−i−ii−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii-1-11111-1-1−iii−i
χ30111-1-11-1-1-1-11111-1-11111-1-1-1-1-1-1111-1-11-111-1-111-1i−i−ii-11i−i−ii−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i11-1-1-1-111i−i−ii
χ31111-1-11-1-1-1-11111-1-11111-1-1-1-1-1-1111-1-11-111-1-111-1−iii−i-11−iii−iii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i-1-11111-1-1i−i−ii
χ32111-1-11-1-1-1-11111-1-11111-1-1-1-1-1-1111-1-11-111-1-111-1−iii−i-11−iii−iii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii11-1-1-1-111−iii−i
χ332222222222222222-2-2-2-2-2-2-2-22222-2-22-2-2-2-2-2-22220000-2-20000000000000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22-2-222222-2-20000220000000000000000000000000000000000000000
χ35222222222222-2-2-2-222-2-222-2-2000022-2-2-20000-20000000000002-22-22-22-20000000000000000000000000000
χ36222222222222-2-2-2-222-2-222-2-2000022-2-2-20000-2000000000000-22-22-22-220000000000000000000000000000
χ37222222222222-2-2-2-2-2-222-2-2220000-2-2-2220000-200222200-2-2-2-2000000000000000000000000000000000000
χ38222222222222-2-2-2-2-2-222-2-2220000-2-2-2220000-200-2-2-2-2002222000000000000000000000000000000000000
χ3922222222-2-2-2-22222222222222222-2-2-2-2-22222-2-2-20000-2-20000000000000000000000000000000000000000
χ4022222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2220000220000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-222-2-222-2-20000-2-2222000020022-2-200-2-222000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-222-2-222-2-20000-2-22220000200-2-2220022-2-2000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-222-2-2220000222-2-2000020000000000002-22-2-22-220000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-222-2-2220000222-2-200002000000000000-22-222-22-20000000000000000000000000000
χ45222-2-22-2-222-2-222-2-22222-2-2-2-222-2-2-222-22-2-222-22-20000-220000000000000000000000000000000000000000
χ46222-2-22-2-222-2-222-2-22222-2-2-2-2-2-222-222-2222-2-2-2-2200002-20000000000000000000000000000000000000000
χ47222-2-22-2-222-2-2-2-22222-2-2-2-2220000-22-22-200002002i−2i2i−2i00−2i2i−2i2i000000000000000000000000000000000000
χ48222-2-22-2-222-2-2-2-22222-2-2-2-2220000-22-22-20000200−2i2i−2i2i002i−2i2i−2i000000000000000000000000000000000000
χ49222-2-22-2-222-2-2-2-222-2-22222-2-200002-2-2-22000020000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ50222-2-22-2-222-2-2-2-222-2-22222-2-200002-2-2-2200002000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ51222-2-22-2-2-2-22222-2-2-2-2-2-2222222-2-2-22-2-2222-2-22-220000-220000000000000000000000000000000000000000
χ52222-2-22-2-2-2-22222-2-2-2-2-2-22222-2-222-22-2-22-2-22222-200002-20000000000000000000000000000000000000000
χ53222-2-22-2-2-2-222-2-22222-2-2-2-22200002-22-220000-20000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ54222-2-22-2-2-2-222-2-22222-2-2-2-22200002-22-220000-2000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ55222-2-22-2-2-2-222-2-222-2-22222-2-20000-2222-20000-2002i−2i−2i2i00−2i2i2i−2i000000000000000000000000000000000000
χ56222-2-22-2-2-2-222-2-222-2-22222-2-20000-2222-20000-200−2i2i2i−2i002i−2i−2i2i000000000000000000000000000000000000
χ5722-22-2-22-200002-22-22i−2i2i−2i2i−2i2i−2i2-22-2000002i−2i2i−2i0000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ5822-22-2-22-200002-22-22i−2i2i−2i2i−2i2i−2i2-22-2000002i−2i2i−2i000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ5922-22-2-22-200002-22-22i−2i2i−2i2i−2i2i−2i-22-2200000−2i2i−2i2i0000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ6022-22-2-22-200002-22-22i−2i2i−2i2i−2i2i−2i-22-2200000−2i2i−2i2i000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ6122-22-2-22-200002-22-2−2i2i−2i2i−2i2i−2i2i2-22-200000−2i2i−2i2i0000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ6222-22-2-22-200002-22-2−2i2i−2i2i−2i2i−2i2i2-22-200000−2i2i−2i2i000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ6322-22-2-22-200002-22-2−2i2i−2i2i−2i2i−2i2i-22-22000002i−2i2i−2i0000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ6422-22-2-22-200002-22-2−2i2i−2i2i−2i2i−2i2i-22-22000002i−2i2i−2i000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ6522-2-22-2-2200002-2-222i−2i2i−2i−2i2i−2i2i2-2-2200000−2i2i2i−2i0000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000
χ6622-2-22-2-2200002-2-222i−2i2i−2i−2i2i−2i2i2-2-2200000−2i2i2i−2i000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000
χ6722-2-22-2-2200002-2-222i−2i2i−2i−2i2i−2i2i-222-2000002i−2i−2i2i0000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000
χ6822-2-22-2-2200002-2-222i−2i2i−2i−2i2i−2i2i-222-2000002i−2i−2i2i000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000
χ6922-2-22-2-2200002-2-22−2i2i−2i2i2i−2i2i−2i2-2-22000002i−2i−2i2i0000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000
χ7022-2-22-2-2200002-2-22−2i2i−2i2i2i−2i2i−2i2-2-22000002i−2i−2i2i000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000
χ7122-2-22-2-2200002-2-22−2i2i−2i2i2i−2i2i−2i-222-200000−2i2i2i−2i0000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000
χ7222-2-22-2-2200002-2-22−2i2i−2i2i2i−2i2i−2i-222-200000−2i2i2i−2i000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000
χ7344-44-4-44-40000-44-444i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ7444-44-4-44-40000-44-44−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ7544-4-44-4-440000-444-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ7644-4-44-4-440000-444-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ774-4444-4-4-44-44-40000000000000000000000000000000000000000000000000000002-22-22-22-2000000000000
χ784-4444-4-4-44-44-4000000000000000000000000000000000000000000000000000000-22-22-22-22000000000000
χ794-4444-4-4-4-44-440000000000000000000000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000
χ804-4444-4-4-4-44-44000000000000000000000000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000
χ814-44-4-4-4444-4-440000000000000000000000000000000000000000000000000000002-2-222-2-22000000000000
χ824-44-4-4-4444-4-44000000000000000000000000000000000000000000000000000000-222-2-222-2000000000000
χ834-44-4-4-444-444-40000000000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ844-44-4-4-444-444-4000000000000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ858-8-88-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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