Finite Group Databasebeta

← Group #198110

Character table — Group #198110

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222224444444444488888888888888881616161611112222222244444444444888888888888888816161616
order12222244444422444448888444444888888888844882222224444442244444888844444488888888884488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ31111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111
χ41111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-11111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1
χ511111111111111-1-11-1-11111-1-11111111111-1-1-1-1-1-1-1-111111111111111-1-11-1-11111-1-11111111111-1-1-1-1-1-1-1-1
χ611111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ711111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1
χ811111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111
χ911111111-1-1-1-1-1-1111-1-1ii−i−i1-1ii−i−i11-1-1i−iii−i−i1-1i−i11111111-1-1-1-1-1-1111-1-1ii−i−i1-1ii−i−i11-1-1i−iii−i−i1-1i−i
χ1011111111-1-1-1-1-1-1111-1-1ii−i−i1-1−i−iii-1-111i−iii−i−i-11−ii11111111-1-1-1-1-1-1111-1-1ii−i−i1-1−i−iii-1-111i−iii−i−i-11−ii
χ1111111111-1-1-1-1-1-1111-1-1−i−iii1-1ii−i−i-1-111−ii−i−iii-11i−i11111111-1-1-1-1-1-1111-1-1−i−iii1-1ii−i−i-1-111−ii−i−iii-11i−i
χ1211111111-1-1-1-1-1-1111-1-1−i−iii1-1−i−iii11-1-1−ii−i−iii1-1−ii11111111-1-1-1-1-1-1111-1-1−i−iii1-1−i−iii11-1-1−ii−i−iii1-1−ii
χ1311111111-1-1-1-1-1-1-1-1111ii−i−i-11ii−i−i11-1-1i−i−i−iii-11−ii11111111-1-1-1-1-1-1-1-1111ii−i−i-11ii−i−i11-1-1i−i−i−iii-11−ii
χ1411111111-1-1-1-1-1-1-1-1111ii−i−i-11−i−iii-1-111i−i−i−iii1-1i−i11111111-1-1-1-1-1-1-1-1111ii−i−i-11−i−iii-1-111i−i−i−iii1-1i−i
χ1511111111-1-1-1-1-1-1-1-1111−i−iii-11ii−i−i-1-111−iiii−i−i1-1−ii11111111-1-1-1-1-1-1-1-1111−i−iii-11ii−i−i-1-111−iiii−i−i1-1−ii
χ1611111111-1-1-1-1-1-1-1-1111−i−iii-11−i−iii11-1-1−iiii−i−i-11i−i11111111-1-1-1-1-1-1-1-1111−i−iii-11−i−iii11-1-1−iiii−i−i-11i−i
χ17222222-2-22222-2-200-20022220000000000-2-200000000222222-2-22222-2-200-20022220000000000-2-200000000
χ18222222-2-22222-2-200-200-2-2-2-200000000002200000000222222-2-22222-2-200-200-2-2-2-200000000002200000000
χ19222222-2-2-2-2-2-22200-2002i2i−2i−2i0000000000−2i2i00000000222222-2-2-2-2-2-22200-2002i2i−2i−2i0000000000−2i2i00000000
χ20222222-2-2-2-2-2-22200-200−2i−2i2i2i00000000002i−2i00000000222222-2-2-2-2-2-22200-200−2i−2i2i2i00000000002i−2i00000000
χ212222-2-22222-2-2-2222-2-2-20000-220000000000000000002222-2-22222-2-2-2222-2-2-20000-22000000000000000000
χ222222-2-22222-2-2-22-2-2-22200002-20000000000000000002222-2-22222-2-2-22-2-2-22200002-2000000000000000000
χ232222-2-222-2-2222-222-2220000-2-20000000000000000002222-2-222-2-2222-222-2220000-2-2000000000000000000
χ242222-2-222-2-2222-2-2-2-2-2-20000220000000000000000002222-2-222-2-2222-2-2-2-2-2-2000022000000000000000000
χ252222-2-2-2-222-2-22-20020000000000000000002i−2i2i−2i00002222-2-2-2-222-2-22-20020000000000000000002i−2i2i−2i0000
χ262222-2-2-2-222-2-22-2002000000000000000000−2i2i−2i2i00002222-2-2-2-222-2-22-2002000000000000000000−2i2i−2i2i0000
χ272222-2-2-2-2-2-222-220020000000000000000002-2-2200002222-2-2-2-2-2-222-220020000000000000000002-2-220000
χ282222-2-2-2-2-2-222-22002000000000000000000-222-200002222-2-2-2-2-2-222-22002000000000000000000-222-20000
χ292-22-22-2002i−2i2i−2i00000002ζ−2ζ2ζ3−2ζ3001+i−1−i1−i−1+i2−2i2−i200000000002-22-22-2002i−2i2i−2i00000002ζ−2ζ2ζ3−2ζ3001+i−1−i1−i−1+i2−2i2−i20000000000
χ302-22-22-2002i−2i2i−2i00000002ζ−2ζ2ζ3−2ζ300−1−i1+i−1+i1−i−22−i2i200000000002-22-22-2002i−2i2i−2i00000002ζ−2ζ2ζ3−2ζ300−1−i1+i−1+i1−i−22−i2i20000000000
χ312-22-22-2002i−2i2i−2i0000000−2ζ2ζ−2ζ32ζ3001+i−1−i1−i−1+i−22−i2i200000000002-22-22-2002i−2i2i−2i0000000−2ζ2ζ−2ζ32ζ3001+i−1−i1−i−1+i−22−i2i20000000000
χ322-22-22-2002i−2i2i−2i0000000−2ζ2ζ−2ζ32ζ300−1−i1+i−1+i1−i2−2i2−i200000000002-22-22-2002i−2i2i−2i0000000−2ζ2ζ−2ζ32ζ300−1−i1+i−1+i1−i2−2i2−i20000000000
χ332-22-22-200−2i2i−2i2i00000002ζ3−2ζ32ζ−2ζ001−i−1+i1+i−1−i−22i2−i200000000002-22-22-200−2i2i−2i2i00000002ζ3−2ζ32ζ−2ζ001−i−1+i1+i−1−i−22i2−i20000000000
χ342-22-22-200−2i2i−2i2i00000002ζ3−2ζ32ζ−2ζ00−1+i1−i−1−i1+i2−2−i2i200000000002-22-22-200−2i2i−2i2i00000002ζ3−2ζ32ζ−2ζ00−1+i1−i−1−i1+i2−2−i2i20000000000
χ352-22-22-200−2i2i−2i2i0000000−2ζ32ζ3−2ζ2ζ001−i−1+i1+i−1−i2−2−i2i200000000002-22-22-200−2i2i−2i2i0000000−2ζ32ζ3−2ζ2ζ001−i−1+i1+i−1−i2−2−i2i20000000000
χ362-22-22-200−2i2i−2i2i0000000−2ζ32ζ3−2ζ2ζ00−1+i1−i−1−i1+i−22i2−i200000000002-22-22-200−2i2i−2i2i0000000−2ζ32ζ3−2ζ2ζ00−1+i1−i−1−i1+i−22i2−i20000000000
χ374-44-4-44004i−4i−4i4i00000000000000000000000000000004-44-4-44004i−4i−4i4i0000000000000000000000000000000
χ384-44-4-4400−4i4i4i−4i00000000000000000000000000000004-44-4-4400−4i4i4i−4i0000000000000000000000000000000
χ394-4-44004-40000000004i−4i0000000000000000000000004-4-44004-40000000004i−4i000000000000000000000000
χ404-4-44004-4000000000−4i4i0000000000000000000000004-4-44004-4000000000−4i4i000000000000000000000000
χ414-4-4400-440000004i−4i0000000000000000000000000004-4-4400-440000004i−4i000000000000000000000000000
χ424-4-4400-44000000−4i4i0000000000000000000000000004-4-4400-44000000−4i4i000000000000000000000000000
χ4388-8-800000000000000000000000000000000000000088-8-8000000000000000000000000000000000000000
χ441111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ451111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ461111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1
χ471111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-111
χ4811111111111111-1-11-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ4911111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11111111111-1-11111-1-1-1-1
χ5011111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111111111-1-1-1-1111111-1-1-1-1-1-111
χ5111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111111111-1-1-1-111-1-1-1-111-1-1
χ5211111111-1-1-1-1-1-1111-1-1ii−i−i1-1ii−i−i11-1-1i−iii−i−i1-1i−i-1-1-1-1-1-1-1-1111111-1-1-111−i−iii-11−i−iii-1-111−ii−i−iii-11−ii
χ5311111111-1-1-1-1-1-1111-1-1ii−i−i1-1−i−iii-1-111i−iii−i−i-11−ii-1-1-1-1-1-1-1-1111111-1-1-111−i−iii-11ii−i−i11-1-1−ii−i−iii1-1i−i
χ5411111111-1-1-1-1-1-1111-1-1−i−iii1-1ii−i−i-1-111−ii−i−iii-11i−i-1-1-1-1-1-1-1-1111111-1-1-111ii−i−i-11−i−iii11-1-1i−iii−i−i1-1−ii
χ5511111111-1-1-1-1-1-1111-1-1−i−iii1-1−i−iii11-1-1−ii−i−iii1-1−ii-1-1-1-1-1-1-1-1111111-1-1-111ii−i−i-11ii−i−i-1-111i−iii−i−i-11i−i
χ5611111111-1-1-1-1-1-1-1-1111ii−i−i-11ii−i−i11-1-1i−i−i−iii-11−ii-1-1-1-1-1-1-1-111111111-1-1-1−i−iii1-1−i−iii-1-111−iiii−i−i1-1i−i
χ5711111111-1-1-1-1-1-1-1-1111ii−i−i-11−i−iii-1-111i−i−i−iii1-1i−i-1-1-1-1-1-1-1-111111111-1-1-1−i−iii1-1ii−i−i11-1-1−iiii−i−i-11−ii
χ5811111111-1-1-1-1-1-1-1-1111−i−iii-11ii−i−i-1-111−iiii−i−i1-1−ii-1-1-1-1-1-1-1-111111111-1-1-1ii−i−i1-1−i−iii11-1-1i−i−i−iii-11i−i
χ5911111111-1-1-1-1-1-1-1-1111−i−iii-11−i−iii11-1-1−iiii−i−i-11i−i-1-1-1-1-1-1-1-111111111-1-1-1ii−i−i1-1ii−i−i-1-111i−i−i−iii1-1−ii
χ60222222-2-22222-2-200-20022220000000000-2-200000000-2-2-2-2-2-222-2-2-2-22200200-2-2-2-200000000002200000000
χ61222222-2-22222-2-200-200-2-2-2-200000000002200000000-2-2-2-2-2-222-2-2-2-2220020022220000000000-2-200000000
χ62222222-2-2-2-2-2-22200-2002i2i−2i−2i0000000000−2i2i00000000-2-2-2-2-2-2222222-2-200200−2i−2i2i2i00000000002i−2i00000000
χ63222222-2-2-2-2-2-22200-200−2i−2i2i2i00000000002i−2i00000000-2-2-2-2-2-2222222-2-2002002i2i−2i−2i0000000000−2i2i00000000
χ642222-2-22222-2-2-2222-2-2-20000-22000000000000000000-2-2-2-222-2-2-2-2222-2-2-222200002-2000000000000000000
χ652222-2-22222-2-2-22-2-2-22200002-2000000000000000000-2-2-2-222-2-2-2-2222-2222-2-20000-22000000000000000000
χ662222-2-222-2-2222-222-2220000-2-2000000000000000000-2-2-2-222-2-222-2-2-22-2-22-2-2000022000000000000000000
χ672222-2-222-2-2222-2-2-2-2-2-2000022000000000000000000-2-2-2-222-2-222-2-2-22222220000-2-2000000000000000000
χ682222-2-2-2-222-2-22-20020000000000000000002i−2i2i−2i0000-2-2-2-22222-2-222-2200-2000000000000000000−2i2i−2i2i0000
χ692222-2-2-2-222-2-22-2002000000000000000000−2i2i−2i2i0000-2-2-2-22222-2-222-2200-20000000000000000002i−2i2i−2i0000
χ702222-2-2-2-2-2-222-220020000000000000000002-2-220000-2-2-2-2222222-2-22-200-2000000000000000000-222-20000
χ712222-2-2-2-2-2-222-22002000000000000000000-222-20000-2-2-2-2222222-2-22-200-20000000000000000002-2-220000
χ722-22-22-2002i−2i2i−2i00000002ζ−2ζ2ζ3−2ζ3001+i−1−i1−i−1+i2−2i2−i20000000000-22-22-2200−2i2i−2i2i0000000−2ζ2ζ−2ζ32ζ300−1−i1+i−1+i1−i−22−i2i20000000000
χ732-22-22-2002i−2i2i−2i00000002ζ−2ζ2ζ3−2ζ300−1−i1+i−1+i1−i−22−i2i20000000000-22-22-2200−2i2i−2i2i0000000−2ζ2ζ−2ζ32ζ3001+i−1−i1−i−1+i2−2i2−i20000000000
χ742-22-22-2002i−2i2i−2i0000000−2ζ2ζ−2ζ32ζ3001+i−1−i1−i−1+i−22−i2i20000000000-22-22-2200−2i2i−2i2i00000002ζ−2ζ2ζ3−2ζ300−1−i1+i−1+i1−i2−2i2−i20000000000
χ752-22-22-2002i−2i2i−2i0000000−2ζ2ζ−2ζ32ζ300−1−i1+i−1+i1−i2−2i2−i20000000000-22-22-2200−2i2i−2i2i00000002ζ−2ζ2ζ3−2ζ3001+i−1−i1−i−1+i−22−i2i20000000000
χ762-22-22-200−2i2i−2i2i00000002ζ3−2ζ32ζ−2ζ001−i−1+i1+i−1−i−22i2−i20000000000-22-22-22002i−2i2i−2i0000000−2ζ32ζ3−2ζ2ζ00−1+i1−i−1−i1+i2−2−i2i20000000000
χ772-22-22-200−2i2i−2i2i00000002ζ3−2ζ32ζ−2ζ00−1+i1−i−1−i1+i2−2−i2i20000000000-22-22-22002i−2i2i−2i0000000−2ζ32ζ3−2ζ2ζ001−i−1+i1+i−1−i−22i2−i20000000000
χ782-22-22-200−2i2i−2i2i0000000−2ζ32ζ3−2ζ2ζ001−i−1+i1+i−1−i2−2−i2i20000000000-22-22-22002i−2i2i−2i00000002ζ3−2ζ32ζ−2ζ00−1+i1−i−1−i1+i−22i2−i20000000000
χ792-22-22-200−2i2i−2i2i0000000−2ζ32ζ3−2ζ2ζ00−1+i1−i−1−i1+i−22i2−i20000000000-22-22-22002i−2i2i−2i00000002ζ3−2ζ32ζ−2ζ001−i−1+i1+i−1−i2−2−i2i20000000000
χ804-44-4-44004i−4i−4i4i0000000000000000000000000000000-44-444-400−4i4i4i−4i0000000000000000000000000000000
χ814-44-4-4400−4i4i4i−4i0000000000000000000000000000000-44-444-4004i−4i−4i4i0000000000000000000000000000000
χ824-4-44004-40000000004i−4i000000000000000000000000-444-400-44000000000−4i4i000000000000000000000000
χ834-4-44004-4000000000−4i4i000000000000000000000000-444-400-440000000004i−4i000000000000000000000000
χ844-4-4400-440000004i−4i000000000000000000000000000-444-4004-4000000−4i4i000000000000000000000000000
χ854-4-4400-44000000−4i4i000000000000000000000000000-444-4004-40000004i−4i000000000000000000000000000
χ8688-8-8000000000000000000000000000000000000000-8-888000000000000000000000000000000000000000

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