Finite Group Databasebeta

← Group #106954

Character table — Group #106954

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222444444444444448888888888888888888888888888888888888888888816161616
order12222222222244444444444444444444444444222244444444444444448888888888888888888888884444
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
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ711111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-1-1-1-1-111-1111111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i
χ1011111111-1-1-1-11111-1-1-1-1-1-1-1-111-1111111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−iii
χ1111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii
χ1211111111-1-1-1-11111-1-1-1-1-1-1-1-111-1111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i
χ1311111111-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iii
χ1411111111-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iii−i−i
χ1511111111-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i
χ1611111111-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−iii
χ17111-1-1-1-1111-1-111-1-111-1-1-111-11-1-11-111-1-111-1-111-11-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-1i−ii−i
χ18111-1-1-1-1111-1-111-1-111-1-1-111-11-1-11-111-1-111-1-111-11-1ii−i−iii−i−iii−i−iii−i−i-1-111-1-111−i−iii−i−iii-1-111-1-111−ii−ii
χ19111-1-1-1-1111-1-111-1-111-1-1-111-11-1-11-111-1-111-1-111-11-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii11-1-111-1-1−ii−ii
χ20111-1-1-1-1111-1-111-1-111-1-1-111-11-1-11-111-1-111-1-111-11-1−i−iii−i−iii−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-1-111-1-111i−ii−i
χ21111-1-1-1-1111-1-111-1-111-1-1-111-11-1-11-1-1-111-1-1111-11-11ii−i−iii−i−i−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i-1-111-1-111−ii−ii
χ22111-1-1-1-1111-1-111-1-111-1-1-111-11-1-11-1-1-111-1-1111-11-11ii−i−iii−i−i−i−iii−i−iii-1-111-1-111−i−iii−i−iii11-1-111-1-1i−ii−i
χ23111-1-1-1-1111-1-111-1-111-1-1-111-11-1-11-1-1-111-1-1111-11-11−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1−i−iii−i−iii-1-111-1-111i−ii−i
χ24111-1-1-1-1111-1-111-1-111-1-1-111-11-1-11-1-1-111-1-1111-11-11−i−iii−i−iiiii−i−iii−i−i-1-111-1-111ii−i−iii−i−i11-1-111-1-1−ii−ii
χ25111-1-1-1-11-1-11111-1-1-1-1111-1-111-111-111-1-1-1-111-11-1-11ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii-111-1
χ26111-1-1-1-11-1-11111-1-1-1-1111-1-111-111-111-1-1-1-111-11-1-11ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i1-1-11
χ27111-1-1-1-11-1-11111-1-1-1-1111-1-111-111-111-1-1-1-111-11-1-11−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii1-1-11
χ28111-1-1-1-11-1-11111-1-1-1-1111-1-111-111-111-1-1-1-111-11-1-11−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i-111-1
χ29111-1-1-1-11-1-11111-1-1-1-1111-1-111-111-1-1-11111-1-1-1-111-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i1-1-11
χ30111-1-1-1-11-1-11111-1-1-1-1111-1-111-111-1-1-11111-1-1-1-111-1ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii-111-1
χ31111-1-1-1-11-1-11111-1-1-1-1111-1-111-111-1-1-11111-1-1-1-111-1−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i-111-1
χ32111-1-1-1-11-1-11111-1-1-1-1111-1-111-111-1-1-11111-1-1-1-111-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii1-1-11
χ332222222222222222222-2-2-2-22-2-2-2-2-222222222-2-2-2-2-200000000000000000000000000000000000000000000
χ342222222222222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-22222-2-2-2-22200000000-20000000000002-22-22-22-20000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-22222-2-2-2-22200000000-2000000000000-22-22-22-220000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-200000000200002-22-22-22-2000000000000000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-20000000020000-22-22-22-22000000000000000000000000000000000000
χ3922222222-2-2-2-22222-2-2-22222-2-2-22-2-22222-2-2-2-22-2-22200000000000000000000000000000000000000000000
χ4022222222-2-2-2-22222-2-2-22222-2-2-22-2-2-2-2-2-22222222-2-200000000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-22222222222-2-2-200000000-200002-22-2-22-22000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-22222222222-2-2-200000000-20000-22-222-22-2000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2222-2-2-2-22-2-22220000000020000000000002-22-2-22-220000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2222-2-2-2-22-2-2222000000002000000000000-22-222-22-20000000000000000000000000000
χ45222-2-2-2-2222-2-222-2-222-222-2-2-2-222-2222-2-222-2-2-2-22-2200000000000000000000000000000000000000000000
χ46222-2-2-2-2222-2-222-2-222-222-2-2-2-222-22-2-222-2-222-22-22-200000000000000000000000000000000000000000000
χ47222-2-2-2-2222-2-2-2-222-2-2222-2-222-2-2-2200000000200002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ48222-2-2-2-2222-2-2-2-222-2-2222-2-222-2-2-220000000020000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ49222-2-2-2-2222-2-2-2-222-2-22-2-2222-2222-200000000-20000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ50222-2-2-2-2222-2-2-2-222-2-22-2-2222-2222-200000000-2000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ51222-2-2-2-22-2-22222-2-2-2-22-2-2222-22-2-2222-2-2-2-2222-222-200000000000000000000000000000000000000000000
χ52222-2-2-2-22-2-22222-2-2-2-22-2-2222-22-2-22-2-22222-2-222-2-2200000000000000000000000000000000000000000000
χ53222-2-2-2-22-2-222-2-22222-222-2-2-2-22-22-20000000020000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ54222-2-2-2-22-2-222-2-22222-222-2-2-2-22-22-2000000002000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ55222-2-2-2-22-2-222-2-22222-2-2-222-22-22-2200000000-200002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ56222-2-2-2-22-2-222-2-22222-2-2-222-22-22-2200000000-20000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ5722-222-2-2-22-22-22-22-22-2-200002000002i−2i2i−2i2i−2i2i−2i0000000000000000000002−22−22−22−200000000i2−i2i2−i2i2−i2i2−i20000
χ5822-222-2-2-22-22-22-22-22-2-200002000002i−2i2i−2i2i−2i2i−2i000000000000000000000−22−22−22−2200000000−i2i2−i2i2−i2i2−i2i20000
χ5922-222-2-2-22-22-22-22-22-2-20000200000−2i2i−2i2i−2i2i−2i2i0000000000000000000002−22−22−22−200000000−i2i2−i2i2−i2i2−i2i20000
χ6022-222-2-2-22-22-22-22-22-2-20000200000−2i2i−2i2i−2i2i−2i2i000000000000000000000−22−22−22−2200000000i2−i2i2−i2i2−i2i2−i20000
χ6122-222-2-2-2-22-222-22-2-2220000-2000002i−2i2i−2i−2i2i−2i2i000000000000000000000i2−i2i2−i2−i2i2−i2i200000000−22−222−22−20000
χ6222-222-2-2-2-22-222-22-2-2220000-2000002i−2i2i−2i−2i2i−2i2i000000000000000000000−i2i2−i2i2i2−i2i2−i2000000002−22−2−22−220000
χ6322-222-2-2-2-22-222-22-2-2220000-200000−2i2i−2i2i2i−2i2i−2i000000000000000000000i2−i2i2−i2−i2i2−i2i2000000002−22−2−22−220000
χ6422-222-2-2-2-22-222-22-2-2220000-200000−2i2i−2i2i2i−2i2i−2i000000000000000000000−i2i2−i2i2i2−i2i2−i200000000−22−222−22−20000
χ6522-2-2-222-22-2-222-2-222-220000-2000002i−2i−2i2i2i−2i−2i2i0000000000000000000002−2−222−2−2200000000i2−i2−i2i2i2−i2−i2i20000
χ6622-2-2-222-22-2-222-2-222-220000-2000002i−2i−2i2i2i−2i−2i2i000000000000000000000−222−2−222−200000000−i2i2i2−i2−i2i2i2−i20000
χ6722-2-2-222-22-2-222-2-222-220000-200000−2i2i2i−2i−2i2i2i−2i0000000000000000000002−2−222−2−2200000000−i2i2i2−i2−i2i2i2−i20000
χ6822-2-2-222-22-2-222-2-222-220000-200000−2i2i2i−2i−2i2i2i−2i000000000000000000000−222−2−222−200000000i2−i2−i2i2i2−i2−i2i20000
χ6922-2-2-222-2-222-22-2-22-22-200002000002i−2i−2i2i−2i2i2i−2i000000000000000000000i2−i2−i2i2−i2i2i2−i200000000−222−22−2−220000
χ7022-2-2-222-2-222-22-2-22-22-200002000002i−2i−2i2i−2i2i2i−2i000000000000000000000−i2i2i2−i2i2−i2−i2i2000000002−2−22−222−20000
χ7122-2-2-222-2-222-22-2-22-22-20000200000−2i2i2i−2i2i−2i−2i2i000000000000000000000i2−i2−i2i2−i2i2i2−i2000000002−2−22−222−20000
χ7222-2-2-222-2-222-22-2-22-22-20000200000−2i2i2i−2i2i−2i−2i2i000000000000000000000−i2i2i2−i2i2−i2−i2i200000000−222−22−2−220000
χ7344-444-4-4-44-44-4-44-44-4440000-400000000000000000000000000000000000000000000000000000000000000
χ7444-444-4-4-4-44-44-44-444-4-40000400000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-444-44-4-44-444-4-44-40000400000000000000000000000000000000000000000000000000000000000000
χ7644-4-4-444-4-444-4-444-44-440000-400000000000000000000000000000000000000000000000000000000000000
χ774-444-44-4-4000000000004i−4i4i−4i00000000000000000000000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000
χ784-444-44-4-4000000000004i−4i4i−4i0000000000000000000000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000
χ794-444-44-4-400000000000−4i4i−4i4i00000000000000000000000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000
χ804-444-44-4-400000000000−4i4i−4i4i0000000000000000000000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000
χ814-44-44-44-4000000000004i−4i−4i4i00000000000000000000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000
χ824-44-44-44-4000000000004i−4i−4i4i0000000000000000000000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000
χ834-44-44-44-400000000000−4i4i4i−4i00000000000000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000
χ844-44-44-44-400000000000−4i4i4i−4i0000000000000000000000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000
χ858-8-88-8-888000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.