Finite Group Databasebeta

← Group #164247

Character table — Group #164247

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111111112222222222224444444444444444444444444488888888888888888888888888816161616161616161616
order12222222444444444444224444444444444444888888884444444888888888888888888884444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ511111111111111111111-1-111-1-111-1-1-1-111-1-1-1-111111111-1-1111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1
χ611111111111111111111-1-111-1-111-1-1-1-111-1-1-1-111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ711111111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111
χ811111111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1iiii−i−i−i−i-1-1111-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-11-1i−ii−i
χ10111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1iiii−i−i−i−i-1-11-1-111ii−i−iiiii−i−i−i−i−i−i−i−iiiii-11-11-11−ii−ii
χ11111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1−i−i−i−iiiii-1-1111-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii1-11-11-1−ii−ii
χ12111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1−i−i−i−iiiii-1-11-1-111−i−iii−i−i−i−iiiiiiiii−i−i−i−i-11-11-11i−ii−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111iiii−i−i−i−i11111-1-1ii−i−i−i−i−i−iiiiiiiii−i−i−i−i-111-1-11−ii−ii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111iiii−i−i−i−i111-1-111ii−i−i−i−i−i−iiiii−i−i−i−iiiii1-1-111-1i−ii−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111−i−i−i−iiiii11111-1-1−i−iiiiiii−i−i−i−i−i−i−i−iiiii-111-1-11i−ii−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111−i−i−i−iiiii111-1-111−i−iiiiiii−i−i−i−iiiii−i−i−i−i1-1-111-1−ii−ii
χ1711111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111111111111-1-11111-1-1-1-111-1-111-1-111-1-111-1-1-1-1-1-111-1-111
χ1811111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1111111-1-111-1-1
χ1911111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-111111111-1-111-1-111-1-111-1-111-1-1-1-11111-1-1
χ2011111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-111-1-11111-1-111-1-11111-1-1-1-111
χ2111111111-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-111111111-11-11111-1-1-1-1-1-111-1-11111-1-111-1-111-1-1-1-111-1-1
χ2211111111-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-111111111-11-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-111
χ2311111111-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-11111111111-1-111-1-1-1-111-1-11111-1-1-1-1-1-111
χ2411111111-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1111111-1-111-1-111-1-111-1-1-1-1111111-1-1
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1iiii−i−i−i−i-11-111-1-1−i−iiiii−i−i−i−iiiii−i−i−i−iii-11-111-1−iii−i
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1iiii−i−i−i−i-11-1-1-111−i−iiiii−i−i−i−iii−i−iiiii−i−i1-11-1-11i−i−ii
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1−i−i−i−iiiii-11-111-1-1ii−i−i−i−iiiii−i−i−i−iiiii−i−i-11-111-1i−i−ii
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1−i−i−i−iiiii-11-1-1-111ii−i−i−i−iiiii−i−iii−i−i−i−iii1-11-1-11−iii−i
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111iiii−i−i−i−i1-1-111-1-1−i−iii−i−iiiii−i−iii−i−i−i−iii1-1-11-11i−i−ii
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111iiii−i−i−i−i1-1-1-1-111−i−iii−i−iiiii−i−i−i−iiiii−i−i-111-11-1−iii−i
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111−i−i−i−iiiii1-1-111-1-1ii−i−iii−i−i−i−iii−i−iiiii−i−i1-1-11-11−iii−i
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111−i−i−i−iiiii1-1-1-1-111ii−i−iii−i−i−i−iiiii−i−i−i−iii-111-11-1i−i−ii
χ3322222222222222-2-2-2-22222-2-222-2-2-2-22222-2-22200000000-2-2-20000000000000000000000000000000000
χ3422222222222222-2-2-2-222-2-2-2-2-2-2-2-222-2-22222-2-20000000022-20000000000000000000000000000000000
χ35222222222222-2-22222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-20000000000000000000000000000000000
χ36222222222222-2-22222-2-2-2-222-2-2-2-22222-2-2222200000000-2-2-20000000000000000000000000000000000
χ3722222222-2-2-2-222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2222200000000-2220000000000000000000000000000000000
χ3822222222-2-2-2-222-2-2-2-222-2-22222-2-22222-2-2-2-2-2-2000000002-220000000000000000000000000000000000
χ3922222222-2-2-2-2-2-22222-2-222-2-2-2-2-2-2-2-2222222-2-2000000002-220000000000000000000000000000000000
χ4022222222-2-2-2-2-2-22222-2-2-2-2-2-222-2-222-2-222-2-22200000000-2220000000000000000000000000000000000
χ4122-2-22-22-200002i−2i2i2i−2i−2i2i−2i0000002-200000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30002-22i−2i0000000000002ζ−2ζ002ζ3−2ζ3000000000000
χ4222-2-22-22-200002i−2i2i2i−2i−2i2i−2i0000002-200000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000-22−2i2i000000000000−2ζ2ζ00−2ζ32ζ3000000000000
χ4322-2-22-22-200002i−2i2i2i−2i−2i2i−2i0000002-20000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30002-22i−2i000000000000−2ζ2ζ00−2ζ32ζ3000000000000
χ4422-2-22-22-200002i−2i2i2i−2i−2i2i−2i0000002-20000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000-22−2i2i0000000000002ζ−2ζ002ζ3−2ζ3000000000000
χ4522-2-22-22-20000−2i2i−2i−2i2i2i−2i2i0000002-200000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0002-2−2i2i0000000000002ζ3−2ζ3002ζ−2ζ000000000000
χ4622-2-22-22-20000−2i2i−2i−2i2i2i−2i2i0000002-200000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000-222i−2i000000000000−2ζ32ζ300−2ζ2ζ000000000000
χ4722-2-22-22-20000−2i2i−2i−2i2i2i−2i2i0000002-20000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0002-2−2i2i000000000000−2ζ32ζ300−2ζ2ζ000000000000
χ4822-2-22-22-20000−2i2i−2i−2i2i2i−2i2i0000002-20000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000-222i−2i0000000000002ζ3−2ζ3002ζ−2ζ000000000000
χ492-22-2-222-22i2i−2i−2i2i−2i0000−2i2i2-2002i−2i00002-22-2002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000001+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000000000
χ502-22-2-222-22i2i−2i−2i2i−2i0000−2i2i2-2002i−2i00002-22-2002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000000000
χ512-22-2-222-22i2i−2i−2i2i−2i0000−2i2i-2200−2i2i0000-222-200−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000001+i−1−i1−i−1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000000000
χ522-22-2-222-22i2i−2i−2i2i−2i0000−2i2i-2200−2i2i0000-222-200−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000000000
χ532-22-2-222-22i2i−2i−2i−2i2i00002i−2i2-2002i−2i0000-22-2200−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i000000000000000000
χ542-22-2-222-22i2i−2i−2i−2i2i00002i−2i2-2002i−2i0000-22-2200−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000001−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i000000000000000000
χ552-22-2-222-22i2i−2i−2i−2i2i00002i−2i-2200−2i2i00002-2-22002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000−1+i1−i−1−i1+i−1−i1+i1−i−1+i−1+i1−i1+i−1−i000000000000000000
χ562-22-2-222-22i2i−2i−2i−2i2i00002i−2i-2200−2i2i00002-2-22002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000001−i−1+i1+i−1−i1+i−1−i−1+i1−i1−i−1+i−1−i1+i000000000000000000
χ572-22-2-222-2−2i−2i2i2i2i−2i0000−2i2i2-200−2i2i0000-22-22002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i000000000000000000
χ582-22-2-222-2−2i−2i2i2i2i−2i0000−2i2i2-200−2i2i0000-22-22002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000001+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i000000000000000000
χ592-22-2-222-2−2i−2i2i2i2i−2i0000−2i2i-22002i−2i00002-2-2200−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000−1−i1+i−1+i1−i−1+i1−i1+i−1−i−1−i1+i1−i−1+i000000000000000000
χ602-22-2-222-2−2i−2i2i2i2i−2i0000−2i2i-22002i−2i00002-2-2200−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000001+i−1−i1−i−1+i1−i−1+i−1−i1+i1+i−1−i−1+i1−i000000000000000000
χ612-22-2-222-2−2i−2i2i2i−2i2i00002i−2i2-200−2i2i00002-22-200−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000001−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000000000
χ622-22-2-222-2−2i−2i2i2i−2i2i00002i−2i2-200−2i2i00002-22-200−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000000000
χ632-22-2-222-2−2i−2i2i2i−2i2i00002i−2i-22002i−2i0000-222-2002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000001−i−1+i1+i−1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000000000
χ642-22-2-222-2−2i−2i2i2i−2i2i00002i−2i-22002i−2i0000-222-2002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000000000
χ654444-4-4-4-44-44-4004-44-400004-400000000000000000000000000000000000000000000000000000000000
χ664444-4-4-4-44-44-400-44-440000-4400000000000000000000000000000000000000000000000000000000000
χ674444-4-4-4-4-44-44004-44-40000-4400000000000000000000000000000000000000000000000000000000000
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χ7044-4-44-44-40000−4i4i4i4i−4i−4i−4i4i000000-440000000000000000000000000000000000000000000000000000000
χ7144-4-4-44-440000004i−4i−4i4i00000000000000000000000000000000000000000000000002+2i−2−2i002−2i−2+2i0000000000
χ7244-4-4-44-440000004i−4i−4i4i0000000000000000000000000000000000000000000000000−2−2i2+2i00−2+2i2−2i0000000000
χ7344-4-4-44-44000000−4i4i4i−4i00000000000000000000000000000000000000000000000002−2i−2+2i002+2i−2−2i0000000000
χ7444-4-4-44-44000000−4i4i4i−4i0000000000000000000000000000000000000000000000000−2+2i2−2i00−2−2i2+2i0000000000
χ754-44-44-4-444i−4i−4i4i00000000000000004-400004i−4i00000000000000000000000000000000000000000000000
χ764-44-44-4-444i−4i−4i4i0000000000000000-440000−4i4i00000000000000000000000000000000000000000000000
χ774-44-44-4-44−4i4i4i−4i00000000000000004-40000−4i4i00000000000000000000000000000000000000000000000
χ784-44-44-4-44−4i4i4i−4i0000000000000000-4400004i−4i00000000000000000000000000000000000000000000000
χ794-4-44-4-4440000440000-4-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000
χ804-4-44-4-4440000440000-4-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000
χ814-4-44-4-4440000-4-400004400000000000000000022−22−2222−222222−220000000000000000000000000000000000000
χ824-4-44-4-4440000-4-4000044000000000000000000−222222−2222−22−22220000000000000000000000000000000000000
χ838-8-8888-8-8000000000000000000000000000000000000000000000000000000000000000000000000000

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