Finite Group Databasebeta

← Group #198708

Character table — Group #198708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222224444444444488888888888888881616161611112222222244444444444888888888888888816161616
order12222222224444444444444224444448888888844442222222222444444444444422444444888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-11-1-1-1-111-1-111111111-1-1-1-1111111111111111111-1-1-1-11-1-1-1-111-1-111111111-1-1-1-1
χ4111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-111-1-111111111111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-111-1-1
χ611111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-11111-1-11111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-11111-1-111
χ711111111111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111
χ811111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-1
χ9111111-1-1-1-1-1-11-1ii−i−iii−i−i11-11-1i−ii−iii−i−i11-1-11-1i−i111111-1-1-1-1-1-11-1ii−i−iii−i−i11-11-1i−ii−iii−i−i11-1-11-1i−i
χ10111111-1-1-1-1-1-11-1ii−i−iii−i−i11-11-1i−ii−i−i−iii-1-111-11−ii111111-1-1-1-1-1-11-1ii−i−iii−i−i11-11-1i−ii−i−i−iii-1-111-11−ii
χ11111111-1-1-1-1-1-11-1ii−i−i−i−iii1-11-11i−i−iiii−i−i11-1-1-11−ii111111-1-1-1-1-1-11-1ii−i−i−i−iii1-11-11i−i−iiii−i−i11-1-1-11−ii
χ12111111-1-1-1-1-1-11-1ii−i−i−i−iii1-11-11i−i−ii−i−iii-1-1111-1i−i111111-1-1-1-1-1-11-1ii−i−i−i−iii1-11-11i−i−ii−i−iii-1-1111-1i−i
χ13111111-1-1-1-1-1-11-1−i−iiiii−i−i1-11-11−iii−iii−i−i-1-1111-1−ii111111-1-1-1-1-1-11-1−i−iiiii−i−i1-11-11−iii−iii−i−i-1-1111-1−ii
χ14111111-1-1-1-1-1-11-1−i−iiiii−i−i1-11-11−iii−i−i−iii11-1-1-11i−i111111-1-1-1-1-1-11-1−i−iiiii−i−i1-11-11−iii−i−i−iii11-1-1-11i−i
χ15111111-1-1-1-1-1-11-1−i−iii−i−iii11-11-1−ii−iiii−i−i-1-111-11i−i111111-1-1-1-1-1-11-1−i−iii−i−iii11-11-1−ii−iiii−i−i-1-111-11i−i
χ16111111-1-1-1-1-1-11-1−i−iii−i−iii11-11-1−ii−ii−i−iii11-1-11-1−ii111111-1-1-1-1-1-11-1−i−iii−i−iii11-11-1−ii−ii−i−iii11-1-11-1−ii
χ172222222222-2-2-2-222220000-20000-2-2000000000000002222222222-2-2-2-222220000-20000-2-200000000000000
χ182222222222-2-2-2-2-2-2-2-20000-2000022000000000000002222222222-2-2-2-2-2-2-2-20000-200002200000000000000
χ19222222-2-2-2-222-222i2i−2i−2i0000-20000−2i2i00000000000000222222-2-2-2-222-222i2i−2i−2i0000-20000−2i2i00000000000000
χ20222222-2-2-2-222-22−2i−2i2i2i0000-200002i−2i00000000000000222222-2-2-2-222-22−2i−2i2i2i0000-200002i−2i00000000000000
χ212222-2-22-22-222-2-20000000022-2-2200000000000000002222-2-22-22-222-2-20000000022-2-220000000000000000
χ222222-2-22-22-222-2-2000000002-222-200000000000000002222-2-22-22-222-2-2000000002-222-20000000000000000
χ232222-2-22-22-2-2-22200002i2i−2i−2i-2000000−2i2i0000000000002222-2-22-22-2-2-22200002i2i−2i−2i-2000000−2i2i000000000000
χ242222-2-22-22-2-2-2220000−2i−2i2i2i-20000002i−2i0000000000002222-2-22-22-2-2-2220000−2i−2i2i2i-20000002i−2i000000000000
χ252222-2-2-22-22222-200002222-2000000-2-20000000000002222-2-2-22-22222-200002222-2000000-2-2000000000000
χ262222-2-2-22-22222-20000-2-2-2-2-2000000220000000000002222-2-2-22-22222-20000-2-2-2-2-200000022000000000000
χ272222-2-2-22-22-2-2-2200000000222-2-200000000000000002222-2-2-22-22-2-2-2200000000222-2-20000000000000000
χ282222-2-2-22-22-2-2-22000000002-2-22200000000000000002222-2-2-22-22-2-2-22000000002-2-2220000000000000000
χ2922-2-22-22-2-2200002-22-20000000000000i2−i2i2−i2i2−i2i2−i2000022-2-22-22-2-2200002-22-20000000000000i2−i2i2−i2i2−i2i2−i20000
χ3022-2-22-22-2-2200002-22-20000000000000−i2i2−i2i2−i2i2−i2i2000022-2-22-22-2-2200002-22-20000000000000−i2i2−i2i2−i2i2−i2i20000
χ3122-2-22-22-2-220000-22-220000000000000i2−i2i2−i2−i2i2−i2i2000022-2-22-22-2-220000-22-220000000000000i2−i2i2−i2−i2i2−i2i20000
χ3222-2-22-22-2-220000-22-220000000000000−i2i2−i2i2i2−i2i2−i2000022-2-22-22-2-220000-22-220000000000000−i2i2−i2i2i2−i2i2−i20000
χ3322-2-22-2-222-200002i−2i−2i2i00000000000002−2−22−i2i2i2−i2000022-2-22-2-222-200002i−2i−2i2i00000000000002−2−22−i2i2i2−i20000
χ3422-2-22-2-222-200002i−2i−2i2i0000000000000−222−2i2−i2−i2i2000022-2-22-2-222-200002i−2i−2i2i0000000000000−222−2i2−i2−i2i20000
χ3522-2-22-2-222-20000−2i2i2i−2i00000000000002−2−22i2−i2−i2i2000022-2-22-2-222-20000−2i2i2i−2i00000000000002−2−22i2−i2−i2i20000
χ3622-2-22-2-222-20000−2i2i2i−2i0000000000000−222−2−i2i2i2−i2000022-2-22-2-222-20000−2i2i2i−2i0000000000000−222−2−i2i2i2−i20000
χ3744-4-4-4444-4-400000000000000000000000000000000044-4-4-4444-4-4000000000000000000000000000000000
χ3844-4-4-44-4-44400000000000000000000000000000000044-4-4-44-4-444000000000000000000000000000000000
χ394-44-40000004i−4i0000002+2i−2−2i2−2i−2+2i0000000000000000000004-44-40000004i−4i0000002+2i−2−2i2−2i−2+2i000000000000000000000
χ404-44-40000004i−4i000000−2−2i2+2i−2+2i2−2i0000000000000000000004-44-40000004i−4i000000−2−2i2+2i−2+2i2−2i000000000000000000000
χ414-44-4000000−4i4i0000002−2i−2+2i2+2i−2−2i0000000000000000000004-44-4000000−4i4i0000002−2i−2+2i2+2i−2−2i000000000000000000000
χ424-44-4000000−4i4i000000−2+2i2−2i−2−2i2+2i0000000000000000000004-44-4000000−4i4i000000−2+2i2−2i−2−2i2+2i000000000000000000000
χ438-8-880000000000000000000000000000000000000008-8-88000000000000000000000000000000000000000
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
χ451111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ46111111111111111111-1-1-1-11-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-111-1-1-1-1-1-1-1-11111
χ47111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-11111111111-1-1-1-1
χ4811111111111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-11111-1-111
χ4911111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-11111-1-1-1-111-1-1
χ5011111111111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-1111111-1-1
χ5111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111111111-1-1-1-1-1-111
χ52111111-1-1-1-1-1-11-1ii−i−iii−i−i11-11-1i−ii−iii−i−i11-1-11-1i−i-1-1-1-1-1-1111111-11−i−iii−i−iii-1-11-11−ii−ii−i−iii-1-111-11−ii
χ53111111-1-1-1-1-1-11-1ii−i−iii−i−i11-11-1i−ii−i−i−iii-1-111-11−ii-1-1-1-1-1-1111111-11−i−iii−i−iii-1-11-11−ii−iiii−i−i11-1-11-1i−i
χ54111111-1-1-1-1-1-11-1ii−i−i−i−iii1-11-11i−i−iiii−i−i11-1-1-11−ii-1-1-1-1-1-1111111-11−i−iiiii−i−i-11-11-1−iii−i−i−iii-1-1111-1i−i
χ55111111-1-1-1-1-1-11-1ii−i−i−i−iii1-11-11i−i−ii−i−iii-1-1111-1i−i-1-1-1-1-1-1111111-11−i−iiiii−i−i-11-11-1−iii−iii−i−i11-1-1-11−ii
χ56111111-1-1-1-1-1-11-1−i−iiiii−i−i1-11-11−iii−iii−i−i-1-1111-1−ii-1-1-1-1-1-1111111-11ii−i−i−i−iii-11-11-1i−i−ii−i−iii11-1-1-11i−i
χ57111111-1-1-1-1-1-11-1−i−iiiii−i−i1-11-11−iii−i−i−iii11-1-1-11i−i-1-1-1-1-1-1111111-11ii−i−i−i−iii-11-11-1i−i−iiii−i−i-1-1111-1−ii
χ58111111-1-1-1-1-1-11-1−i−iii−i−iii11-11-1−ii−iiii−i−i-1-111-11i−i-1-1-1-1-1-1111111-11ii−i−iii−i−i-1-11-11i−ii−i−i−iii11-1-11-1−ii
χ59111111-1-1-1-1-1-11-1−i−iii−i−iii11-11-1−ii−ii−i−iii11-1-11-1−ii-1-1-1-1-1-1111111-11ii−i−iii−i−i-1-11-11i−ii−iii−i−i-1-111-11i−i
χ602222222222-2-2-2-222220000-20000-2-200000000000000-2-2-2-2-2-2-2-2-2-22222-2-2-2-20000200002200000000000000
χ612222222222-2-2-2-2-2-2-2-20000-200002200000000000000-2-2-2-2-2-2-2-2-2-222222222000020000-2-200000000000000
χ62222222-2-2-2-222-222i2i−2i−2i0000-20000−2i2i00000000000000-2-2-2-2-2-22222-2-22-2−2i−2i2i2i0000200002i−2i00000000000000
χ63222222-2-2-2-222-22−2i−2i2i2i0000-200002i−2i00000000000000-2-2-2-2-2-22222-2-22-22i2i−2i−2i000020000−2i2i00000000000000
χ642222-2-22-22-222-2-20000000022-2-220000000000000000-2-2-2-222-22-22-2-22200000000-2-222-20000000000000000
χ652222-2-22-22-222-2-2000000002-222-20000000000000000-2-2-2-222-22-22-2-22200000000-22-2-220000000000000000
χ662222-2-22-22-2-2-22200002i2i−2i−2i-2000000−2i2i000000000000-2-2-2-222-22-2222-2-20000−2i−2i2i2i20000002i−2i000000000000
χ672222-2-22-22-2-2-2220000−2i−2i2i2i-20000002i−2i000000000000-2-2-2-222-22-2222-2-200002i2i−2i−2i2000000−2i2i000000000000
χ682222-2-2-22-22222-200002222-2000000-2-2000000000000-2-2-2-2222-22-2-2-2-220000-2-2-2-2200000022000000000000
χ692222-2-2-22-22222-20000-2-2-2-2-200000022000000000000-2-2-2-2222-22-2-2-2-22000022222000000-2-2000000000000
χ702222-2-2-22-22-2-2-2200000000222-2-20000000000000000-2-2-2-2222-22-2222-200000000-2-2-2220000000000000000
χ712222-2-2-22-22-2-2-22000000002-2-2220000000000000000-2-2-2-2222-22-2222-200000000-222-2-20000000000000000
χ7222-2-22-22-2-2200002-22-20000000000000i2−i2i2−i2i2−i2i2−i20000-2-222-22-222-20000-22-220000000000000−i2i2−i2i2−i2i2−i2i20000
χ7322-2-22-22-2-2200002-22-20000000000000−i2i2−i2i2−i2i2−i2i20000-2-222-22-222-20000-22-220000000000000i2−i2i2−i2i2−i2i2−i20000
χ7422-2-22-22-2-220000-22-220000000000000i2−i2i2−i2−i2i2−i2i20000-2-222-22-222-200002-22-20000000000000−i2i2−i2i2i2−i2i2−i20000
χ7522-2-22-22-2-220000-22-220000000000000−i2i2−i2i2i2−i2i2−i20000-2-222-22-222-200002-22-20000000000000i2−i2i2−i2−i2i2−i2i20000
χ7622-2-22-2-222-200002i−2i−2i2i00000000000002−2−22−i2i2i2−i20000-2-222-222-2-220000−2i2i2i−2i0000000000000−222−2i2−i2−i2i20000
χ7722-2-22-2-222-200002i−2i−2i2i0000000000000−222−2i2−i2−i2i20000-2-222-222-2-220000−2i2i2i−2i00000000000002−2−22−i2i2i2−i20000
χ7822-2-22-2-222-20000−2i2i2i−2i00000000000002−2−22i2−i2−i2i20000-2-222-222-2-2200002i−2i−2i2i0000000000000−222−2−i2i2i2−i20000
χ7922-2-22-2-222-20000−2i2i2i−2i0000000000000−222−2−i2i2i2−i20000-2-222-222-2-2200002i−2i−2i2i00000000000002−2−22i2−i2−i2i20000
χ8044-4-4-4444-4-4000000000000000000000000000000000-4-4444-4-4-444000000000000000000000000000000000
χ8144-4-4-44-4-444000000000000000000000000000000000-4-4444-444-4-4000000000000000000000000000000000
χ824-44-40000004i−4i0000002+2i−2−2i2−2i−2+2i000000000000000000000-44-44000000−4i4i000000−2−2i2+2i−2+2i2−2i000000000000000000000
χ834-44-40000004i−4i000000−2−2i2+2i−2+2i2−2i000000000000000000000-44-44000000−4i4i0000002+2i−2−2i2−2i−2+2i000000000000000000000
χ844-44-4000000−4i4i0000002−2i−2+2i2+2i−2−2i000000000000000000000-44-440000004i−4i000000−2+2i2−2i−2−2i2+2i000000000000000000000
χ854-44-4000000−4i4i000000−2+2i2−2i−2−2i2+2i000000000000000000000-44-440000004i−4i0000002−2i−2+2i2+2i−2−2i000000000000000000000
χ868-8-88000000000000000000000000000000000000000-888-8000000000000000000000000000000000000000

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