Finite Group Databasebeta

← Group #209934

Character table — Group #209934

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222444444444444448888888888888888888888888888888888888888888816161616
order12222222444444444444444422224444444444222222444444444444448888888888888888888888884444
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
χ311111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ7111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ91111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ101111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ121111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ131111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ141111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ151111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ161111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ1711-11-1-11-11-1ii−i−i1-1ii−i−i1-11-111-1-1i−ii−iii−i−i1-111-1-11-11-1i−ii−i1-1ii−i−ii−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i
χ1811-11-1-11-11-1ii−i−i1-1ii−i−i1-11-111-1-1i−ii−iii−i−i1-111-1-11-11-1i−ii−i1-1ii−i−ii−i-1-111−i−iii-1-111−i−iii-1-111−i−iii-11−ii
χ1911-11-1-11-11-1ii−i−i1-1ii−i−i1-11-111-1-1i−ii−iii−i−i1-1-1-111-111-1i−i−ii-11−i−iii−ii11-1-1ii−i−i-1-111−i−iii11-1-1ii−i−i-11−ii
χ2011-11-1-11-11-1ii−i−i1-1ii−i−i1-11-111-1-1i−ii−iii−i−i1-1-1-111-111-1i−i−ii-11−i−iii−ii-1-111−i−iii11-1-1ii−i−i-1-111−i−iii1-1i−i
χ2111-11-1-11-11-1ii−i−i1-1ii−i−i1-11-1-1-111i−ii−i−i−iii1-111-1-1-11-11−ii−ii-11ii−i−i−ii11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii-11−ii
χ2211-11-1-11-11-1ii−i−i1-1ii−i−i1-11-1-1-111i−ii−i−i−iii1-111-1-1-11-11−ii−ii-11ii−i−i−ii-1-111−i−iii-1-111−i−iii11-1-1ii−i−i1-1i−i
χ2311-11-1-11-11-1ii−i−i1-1ii−i−i1-11-1-1-111i−ii−i−i−iii1-1-1-1111-1-11−iii−i1-1−i−iiii−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii1-1i−i
χ2411-11-1-11-11-1ii−i−i1-1ii−i−i1-11-1-1-111i−ii−i−i−iii1-1-1-1111-1-11−iii−i1-1−i−iiii−i-1-111−i−iii11-1-1ii−i−i11-1-1ii−i−i-11−ii
χ2511-11-1-11-11-1−i−iii1-1−i−iii1-11-111-1-1−ii−ii−i−iii1-111-1-11-11-1−ii−ii1-1−i−iii−ii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii1-1−ii
χ2611-11-1-11-11-1−i−iii1-1−i−iii1-11-111-1-1−ii−ii−i−iii1-111-1-11-11-1−ii−ii1-1−i−iii−ii-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i-11i−i
χ2711-11-1-11-11-1−i−iii1-1−i−iii1-11-111-1-1−ii−ii−i−iii1-1-1-111-111-1−iii−i-11ii−i−ii−i11-1-1−i−iii-1-111ii−i−i11-1-1−i−iii-11i−i
χ2811-11-1-11-11-1−i−iii1-1−i−iii1-11-111-1-1−ii−ii−i−iii1-1-1-111-111-1−iii−i-11ii−i−ii−i-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i1-1−ii
χ2911-11-1-11-11-1−i−iii1-1−i−iii1-11-1-1-111−ii−iiii−i−i1-111-1-1-11-11i−ii−i-11−i−iiii−i11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i-11i−i
χ3011-11-1-11-11-1−i−iii1-1−i−iii1-11-1-1-111−ii−iiii−i−i1-111-1-1-11-11i−ii−i-11−i−iiii−i-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii1-1−ii
χ3111-11-1-11-11-1−i−iii1-1−i−iii1-11-1-1-111−ii−iiii−i−i1-1-1-1111-1-11i−i−ii1-1ii−i−i−ii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i1-1−ii
χ3211-11-1-11-11-1−i−iii1-1−i−iii1-11-1-1-111−ii−iiii−i−i1-1-1-1111-1-11i−i−ii1-1ii−i−i−ii-1-111ii−i−i11-1-1−i−iii11-1-1−i−iii-11i−i
χ3322222222222222-2-2-2-2-2-222-2-20000-2-2220000-2-20000220000-2-2-2-20000220000000000000000000000000000
χ3422222222222222-2-2-2-2-2-222-2-20000-2-2220000-2-20000-2-2000022220000-2-20000000000000000000000000000
χ352222222222-2-2-2-2-2-2222222-2-2000022-2-20000-2-2000022000022-2-20000-2-20000000000000000000000000000
χ362222222222-2-2-2-2-2-2222222-2-2000022-2-20000-2-20000-2-20000-2-2220000220000000000000000000000000000
χ3722222222-2-22222222222-2-2222222-2-2-2-22222-2-2000000-2-2-2-200000000000000000000000000000000000000
χ3822222222-2-22222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000222200000000000000000000000000000000000000
χ3922222222-2-22222-2-2-2-2-2-2-2-2-2-2000022-2-20000222-22-200000000002-22-2000000000000000000000000000000
χ4022222222-2-22222-2-2-2-2-2-2-2-2-2-2000022-2-2000022-22-220000000000-22-22000000000000000000000000000000
χ4122222222-2-2-2-2-2-222-2-2-2-2-2-22222222222-2-2-2-2-2-2000000-2-22200000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-222-2-2-2-2-2-222-2-2-2-222222222-2-200000022-2-200000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-22222-2-2-2-20000-2-2220000222-22-20000000000-22-22000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-2-2-2-20000-2-222000022-22-2200000000002-22-2000000000000000000000000000000
χ4522-22-2-22-22-22i2i−2i−2i-22−2i−2i2i2i2-2-220000−2i2i2i−2i0000-2200002-20000−2i2i-2200002i−2i0000000000000000000000000000
χ4622-22-2-22-22-22i2i−2i−2i-22−2i−2i2i2i2-2-220000−2i2i2i−2i0000-220000-2200002i−2i2-20000−2i2i0000000000000000000000000000
χ4722-22-2-22-22-2−2i−2i2i2i-222i2i−2i−2i2-2-2200002i−2i−2i2i0000-2200002-200002i−2i-220000−2i2i0000000000000000000000000000
χ4822-22-2-22-22-2−2i−2i2i2i-222i2i−2i−2i2-2-2200002i−2i−2i2i0000-220000-220000−2i2i2-200002i−2i0000000000000000000000000000
χ4922-22-2-22-2-222i2i−2i−2i2-22i2i−2i−2i-222-222-2-2−2i2i−2i2i2i2i−2i−2i-22000000-22−2i2i00000000000000000000000000000000000000
χ5022-22-2-22-2-222i2i−2i−2i2-22i2i−2i−2i-222-2-2-222−2i2i−2i2i−2i−2i2i2i-220000002-22i−2i00000000000000000000000000000000000000
χ5122-22-2-22-2-222i2i−2i−2i-22−2i−2i2i2i-22-2200002i−2i−2i2i00002-22-2-2200000000002i−2i−2i2i000000000000000000000000000000
χ5222-22-2-22-2-222i2i−2i−2i-22−2i−2i2i2i-22-2200002i−2i−2i2i00002-2-222-20000000000−2i2i2i−2i000000000000000000000000000000
χ5322-22-2-22-2-22−2i−2i2i2i2-2−2i−2i2i2i-222-222-2-22i−2i2i−2i−2i−2i2i2i-22000000-222i−2i00000000000000000000000000000000000000
χ5422-22-2-22-2-22−2i−2i2i2i2-2−2i−2i2i2i-222-2-2-2222i−2i2i−2i2i2i−2i−2i-220000002-2−2i2i00000000000000000000000000000000000000
χ5522-22-2-22-2-22−2i−2i2i2i-222i2i−2i−2i-22-220000−2i2i2i−2i00002-22-2-220000000000−2i2i2i−2i000000000000000000000000000000
χ5622-22-2-22-2-22−2i−2i2i2i-222i2i−2i−2i-22-220000−2i2i2i−2i00002-2-222-200000000002i−2i−2i2i000000000000000000000000000000
χ572-22-22-22-2002i−2i2i−2i-222i−2i2i−2i002-22-22-200002i−2i2i−2i00000000000000000000002−22−2i2−i2i2−i2000000002−22−2i2−i2i2−i20000
χ582-22-22-22-2002i−2i2i−2i-222i−2i2i−2i002-22-22-200002i−2i2i−2i0000000000000000000000−22−22−i2i2−i2i200000000−22−22−i2i2−i2i20000
χ592-22-22-22-2002i−2i2i−2i-222i−2i2i−2i002-2-22-220000−2i2i−2i2i00000000000000000000002−22−2i2−i2i2−i200000000−22−22−i2i2−i2i20000
χ602-22-22-22-2002i−2i2i−2i-222i−2i2i−2i002-2-22-220000−2i2i−2i2i0000000000000000000000−22−22−i2i2−i2i2000000002−22−2i2−i2i2−i20000
χ612-22-22-22-200−2i2i−2i2i-22−2i2i−2i2i002-22-22-20000−2i2i−2i2i00000000000000000000002−22−2−i2i2−i2i2000000002−22−2−i2i2−i2i20000
χ622-22-22-22-200−2i2i−2i2i-22−2i2i−2i2i002-22-22-20000−2i2i−2i2i0000000000000000000000−22−22i2−i2i2−i200000000−22−22i2−i2i2−i20000
χ632-22-22-22-200−2i2i−2i2i-22−2i2i−2i2i002-2-22-2200002i−2i2i−2i00000000000000000000002−22−2−i2i2−i2i200000000−22−22i2−i2i2−i20000
χ642-22-22-22-200−2i2i−2i2i-22−2i2i−2i2i002-2-22-2200002i−2i2i−2i0000000000000000000000−22−22i2−i2i2−i2000000002−22−2−i2i2−i2i20000
χ652-2-2-2-2222002-2-22-2-22-2-2200222-2-2200002-2-2200000000000000000000002−2−222−2−22000000002−2−222−2−220000
χ662-2-2-2-2222002-2-22-2-22-2-2200222-2-2200002-2-220000000000000000000000−222−2−222−200000000−222−2−222−20000
χ672-2-2-2-2222002-2-22-2-22-2-220022-222-20000-222-200000000000000000000002−2−222−2−2200000000−222−2−222−20000
χ682-2-2-2-2222002-2-22-2-22-2-220022-222-20000-222-20000000000000000000000−222−2−222−2000000002−2−222−2−220000
χ692-2-2-2-222200-222-2-2-2-222-200222-2-220000-222-200000000000000000000002−2−22−222−2000000002−2−22−222−20000
χ702-2-2-2-222200-222-2-2-2-222-200222-2-220000-222-20000000000000000000000−222−22−2−2200000000−222−22−2−220000
χ712-2-2-2-222200-222-2-2-2-222-20022-222-200002-2-2200000000000000000000002−2−22−222−200000000−222−22−2−220000
χ722-2-2-2-222200-222-2-2-2-222-20022-222-200002-2-220000000000000000000000−222−22−2−22000000002−2−22−222−20000
χ734-444-4-4-44440000000000-4-4000000000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ744-444-4-4-44440000000000-4-400000000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ754-444-4-4-44-4-400000000004400000000000000000000000000000000000000000000000022−2222−22000000000000
χ764-444-4-4-44-4-4000000000044000000000000000000000000000000000000000000000000−2222−2222000000000000
χ774-44-44-44-4004i−4i4i−4i4-4−4i4i−4i4i00-4400000000000000000000000000000000000000000000000000000000000000
χ784-44-44-44-400−4i4i−4i4i4-44i−4i4i−4i00-4400000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-4-44-40000000000-44000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ804-4-4444-4-44-40000000000-4400000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ814-4-4444-4-4-4400000000004-40000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ824-4-4444-4-4-4400000000004-4000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ834-4-4-4-4444004-4-4444-444-400-4-400000000000000000000000000000000000000000000000000000000000000
χ844-4-4-4-444400-444-4444-4-4400-4-400000000000000000000000000000000000000000000000000000000000000
χ85888-8-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-88-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000

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