Finite Group Databasebeta

← Group #106952

Character table — Group #106952

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222444444444444448888888888888888888888888888888888888888888816161616
order12222222222244444444444422222222444444444444444444444444448888888888888888888888884444
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
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ911111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-111-111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i
χ1011111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-111-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−iii
χ1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-111-111-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii
χ1211111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-111-111-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i
χ1311111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iii
χ1411111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iii−i−i
χ1511111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i
χ1611111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−iii
χ171-1-1111-1-111-1-111-1-111-1-1-111-111-1-111-1-11-1-11-111-11-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-1i−ii−i
χ181-1-1111-1-111-1-111-1-111-1-1-111-111-1-111-1-11-1-11-111-11-1ii−i−iii−i−iii−i−iii−i−i-1-111-1-111−i−iii−i−iii-1-111-1-111−ii−ii
χ191-1-1111-1-111-1-111-1-111-1-1-111-111-1-111-1-11-1-11-111-11-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii11-1-111-1-1−ii−ii
χ201-1-1111-1-111-1-111-1-111-1-1-111-111-1-111-1-11-1-11-111-11-1−i−iii−i−iii−i−iii−i−iii-1-111-1-111ii−i−iii−i−i-1-111-1-111i−ii−i
χ211-1-1111-1-111-1-111-1-111-1-1-111-1-1-111-1-1111-1-11-11-11-11ii−i−iii−i−i−i−iii−i−iii11-1-111-1-1ii−i−iii−i−i-1-111-1-111−ii−ii
χ221-1-1111-1-111-1-111-1-111-1-1-111-1-1-111-1-1111-1-11-11-11-11ii−i−iii−i−i−i−iii−i−iii-1-111-1-111−i−iii−i−iii11-1-111-1-1i−ii−i
χ231-1-1111-1-111-1-111-1-111-1-1-111-1-1-111-1-1111-1-11-11-11-11−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1−i−iii−i−iii-1-111-1-111i−ii−i
χ241-1-1111-1-111-1-111-1-111-1-1-111-1-1-111-1-1111-1-11-11-11-11−i−iii−i−iiiii−i−iii−i−i-1-111-1-111ii−i−iii−i−i11-1-111-1-1−ii−ii
χ251-1-1111-1-1-1-11111-1-1-1-1111-1-1111-1-1-1-1111-111-1-11-1-11ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii-111-1
χ261-1-1111-1-1-1-11111-1-1-1-1111-1-1111-1-1-1-1111-111-1-11-1-11ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i1-1-11
χ271-1-1111-1-1-1-11111-1-1-1-1111-1-1111-1-1-1-1111-111-1-11-1-11−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii1-1-11
χ281-1-1111-1-1-1-11111-1-1-1-1111-1-1111-1-1-1-1111-111-1-11-1-11−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i-111-1
χ291-1-1111-1-1-1-11111-1-1-1-1111-1-11-1-11111-1-11-111-1-1-111-1ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i1-1-11
χ301-1-1111-1-1-1-11111-1-1-1-1111-1-11-1-11111-1-11-111-1-1-111-1ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii-111-1
χ311-1-1111-1-1-1-11111-1-1-1-1111-1-11-1-11111-1-11-111-1-1-111-1−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i-111-1
χ321-1-1111-1-1-1-11111-1-1-1-1111-1-11-1-11111-1-11-111-1-1-111-1−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii1-1-11
χ332222222222222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ342222222222222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-22222-200000000-2-2-222-20000000000002-22-22-22-20000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-22222-200000000-2-2-222-2000000000000-22-22-22-220000000000000000000000000000
χ37222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000222-2-2200002-22-22-22-2000000000000000000000000000000000000
χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000222-2-220000-22-22-22-22000000000000000000000000000000000000
χ3922222222-2-2-2-22222-2-2-22222-22222-2-2-2-2-2-22-2-22-2-22200000000000000000000000000000000000000000000
χ4022222222-2-2-2-22222-2-2-22222-2-2-2-2-22222-2-22-2-2222-2-200000000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-2222222220000000022-2-2-2-200002-22-2-22-22000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-2222222220000000022-2-2-2-20000-22-222-22-2000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2222-2-2-2-2200000000-2-222220000000000002-22-2-22-220000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2222-2-2-2-2200000000-2-22222000000000000-22-222-22-20000000000000000000000000000
χ452222-2-2-2-22-22-22-22-22-220000-22-22-22-22-2000000000000000000000000002−22−22−22−2000000002−22−22−22−20000
χ462222-2-2-2-22-22-22-22-22-220000-22-22-22-22-200000000000000000000000000−22−22−22−2200000000−22−22−22−220000
χ472222-2-2-2-22-22-22-22-22-220000-2-22-22-22-22000000000000000000000000002−22−22−22−200000000−22−22−22−220000
χ482222-2-2-2-22-22-22-22-22-220000-2-22-22-22-2200000000000000000000000000−22−22−22−22000000002−22−22−22−20000
χ492222-2-2-2-2-22-222-22-2-22-2000022-22-2-22-2200000000000000000000000000i2−i2i2−i2−i2i2−i2i200000000i2−i2i2−i2−i2i2−i2i20000
χ502222-2-2-2-2-22-222-22-2-22-2000022-22-2-22-2200000000000000000000000000−i2i2−i2i2i2−i2i2−i200000000−i2i2−i2i2i2−i2i2−i20000
χ512222-2-2-2-2-22-222-22-2-22-200002-22-222-22-200000000000000000000000000i2−i2i2−i2−i2i2−i2i200000000−i2i2−i2i2i2−i2i2−i20000
χ522222-2-2-2-2-22-222-22-2-22-200002-22-222-22-200000000000000000000000000−i2i2−i2i2i2−i2i2−i200000000i2−i2i2−i2−i2i2−i2i20000
χ532-2-2222-2-222-2-222-2-222-222-2-2-222-2-222-2-2-222-22-2-22-2200000000000000000000000000000000000000000000
χ542-2-2222-2-222-2-222-2-222-222-2-2-2-2-222-2-222-222-22-22-22-200000000000000000000000000000000000000000000
χ552-2-2222-2-222-2-2-2-222-2-2222-2-22000000002-2-2-22200002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ562-2-2222-2-222-2-2-2-222-2-2222-2-22000000002-2-2-2220000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ572-2-2222-2-222-2-2-2-222-2-22-2-222200000000-2222-2-20000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ582-2-2222-2-222-2-2-2-222-2-22-2-222200000000-2222-2-2000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ592-2-2222-2-2-2-22222-2-2-2-22-2-222222-2-2-2-222-22-2-222-222-200000000000000000000000000000000000000000000
χ602-2-2222-2-2-2-22222-2-2-2-22-2-2222-2-22222-2-2-22-2-2222-2-2200000000000000000000000000000000000000000000
χ612-2-2222-2-2-2-222-2-22222-222-2-2-200000000-22-22-220000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ622-2-2222-2-2-2-222-2-22222-222-2-2-200000000-22-22-22000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ632-2-2222-2-2-2-222-2-22222-2-2-222-2000000002-22-22-200002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ642-2-2222-2-2-2-222-2-22222-2-2-222-2000000002-22-22-20000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ652-2-22-2-2222-2-222-2-222-2-2000022-2-222-2-22000000000000000000000000002−2−222−2−22000000002−2−222−2−220000
χ662-2-22-2-2222-2-222-2-222-2-2000022-2-222-2-2200000000000000000000000000−222−2−222−200000000−222−2−222−20000
χ672-2-22-2-2222-2-222-2-222-2-200002-222-2-222-2000000000000000000000000002−2−222−2−2200000000−222−2−222−20000
χ682-2-22-2-2222-2-222-2-222-2-200002-222-2-222-200000000000000000000000000−222−2−222−2000000002−2−222−2−220000
χ692-2-22-2-222-222-22-2-22-2220000-22-2-22-222-200000000000000000000000000i2−i2−i2i2−i2i2i2−i200000000i2−i2−i2i2−i2i2i2−i20000
χ702-2-22-2-222-222-22-2-22-2220000-22-2-22-222-200000000000000000000000000−i2i2i2−i2i2−i2−i2i200000000−i2i2i2−i2i2−i2−i2i20000
χ712-2-22-2-222-222-22-2-22-2220000-2-222-22-2-2200000000000000000000000000i2−i2−i2i2−i2i2i2−i200000000−i2i2i2−i2i2−i2−i2i20000
χ722-2-22-2-222-222-22-2-22-2220000-2-222-22-2-2200000000000000000000000000−i2i2i2−i2i2−i2−i2i200000000i2−i2−i2i2−i2i2i2−i20000
χ734444-4-4-4-44-44-4-44-44-44-40000400000000000000000000000000000000000000000000000000000000000000
χ744444-4-4-4-4-44-44-44-444-440000-400000000000000000000000000000000000000000000000000000000000000
χ7544-4-44-44-4000000000004i−4i4i−4i00000000000000000000000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000
χ7644-4-44-44-4000000000004i−4i4i−4i0000000000000000000000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000
χ7744-4-44-44-400000000000−4i4i−4i4i00000000000000000000000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000
χ7844-4-44-44-400000000000−4i4i−4i4i0000000000000000000000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000
χ794-44-44-4-44000000000004i−4i−4i4i00000000000000000000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000
χ804-44-44-4-44000000000004i−4i−4i4i0000000000000000000000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000
χ814-44-44-4-4400000000000−4i4i4i−4i00000000000000000000000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000
χ824-44-44-4-4400000000000−4i4i4i−4i0000000000000000000000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000
χ834-4-44-4-4444-4-44-444-4-4440000-400000000000000000000000000000000000000000000000000000000000000
χ844-4-44-4-444-444-4-444-44-4-40000400000000000000000000000000000000000000000000000000000000000000
χ8588-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-88-8-888-8000000000000000000000000000000000000000000000000000000000000000000000000000000

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