Finite Group Databasebeta

← Group #367175

Character table — Group #367175

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222224444444444444444444444444444444488888888888888888888888888881616161616161616
order12222222222222224444444422224444444444448888888888888888444444444444444444448888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ9111111111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ10111111111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ11111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ12111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ171111-1-1111-1-1-1-1-1-11111-1-1-11-111-1-1iiii−i−i−i−i11-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−ii−ii−i1-11-1
χ181111-1-1111-1-1-1-1-1-11111-1-1-11-111-1-1iiii−i−i−i−i11-1-11111-1-1-1-11111-1-1-1-1ii−i−i−i−iii−i−iii-1-111-1-111ii−i−iii−i−i−ii−ii-11-11
χ191111-1-1111-1-1-1-1-1-11111-1-1-11-111-1-1iiii−i−i−i−i11-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−iii−i−i11-1-111-1-1−i−iii−i−iii−ii−ii-11-11
χ201111-1-1111-1-1-1-1-1-11111-1-1-11-111-1-1iiii−i−i−i−i11-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iii−i−iii-1-111-1-111−i−iii−i−iiii−ii−i1-11-1
χ211111-1-1111-1-1-1-1-1-11111-1-1-11-111-1-1−i−i−i−iiiii11-1-11111-1-1-1-11111-1-1-1-1−i−iiiii−i−iii−i−i-1-111-1-111−i−iii−i−iiii−ii−i-11-11
χ221111-1-1111-1-1-1-1-1-11111-1-1-11-111-1-1−i−i−i−iiiii11-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii−ii−ii1-11-1
χ231111-1-1111-1-1-1-1-1-11111-1-1-11-111-1-1−i−i−i−iiiii11-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−iii−i−i-1-111-1-111ii−i−iii−i−i−ii−ii1-11-1
χ241111-1-1111-1-1-1-1-1-11111-1-1-11-111-1-1−i−i−i−iiiii11-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iii−i−iii11-1-111-1-1ii−i−iii−i−ii−ii−i-11-11
χ251111-1-1111-1-1-1-1-1-11111-1-1-11-1-1-111iiii−i−i−i−i-1-1111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iii11-1-1-1-111ii−i−i−i−iiii−i−ii1-1-11
χ261111-1-1111-1-1-1-1-1-11111-1-1-11-1-1-111iiii−i−i−i−i-1-1111111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii−iii−i-111-1
χ271111-1-1111-1-1-1-1-1-11111-1-1-11-1-1-111iiii−i−i−i−i-1-111-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i−iii−i-111-1
χ281111-1-1111-1-1-1-1-1-11111-1-1-11-1-1-111iiii−i−i−i−i-1-111-1-1-1-111111111-1-1-1-1−i−iii−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−ii−i−ii1-1-11
χ291111-1-1111-1-1-1-1-1-11111-1-1-11-1-1-111−i−i−i−iiiii-1-1111111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii-1-11111-1-1−i−iiiii−i−ii−i−ii-111-1
χ301111-1-1111-1-1-1-1-1-11111-1-1-11-1-1-111−i−i−i−iiiii-1-1111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i−iii−i1-1-11
χ311111-1-1111-1-1-1-1-1-11111-1-1-11-1-1-111−i−i−i−iiiii-1-111-1-1-1-111111111-1-1-1-1ii−i−iii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii−iii−i1-1-11
χ321111-1-1111-1-1-1-1-1-11111-1-1-11-1-1-111−i−i−i−iiiii-1-111-1-1-1-111111111-1-1-1-1ii−i−i−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iiii−i−ii-111-1
χ332222222222222222-2-2-2-2-2-2-2-2222222-2-222-2-2-2-2-2-200000000000000002-22-200000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-22222-2-222-2-222-2-2-2-20000000000000000-22-2200000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222220000000000000000-22-2200000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222222200000000000000002-22-200000000000000000000000000000000
χ372222-2-2222-2-2-2-2-2-22-2-2-2222-2222-2-22i2i−2i−2i−2i−2i2i2i-2-22200000000000000002i−2i−2i2i00000000000000000000000000000000
χ382222-2-2222-2-2-2-2-2-22-2-2-2222-2222-2-2−2i−2i2i2i2i2i−2i−2i-2-2220000000000000000−2i2i2i−2i00000000000000000000000000000000
χ392222-2-2222-2-2-2-2-2-22-2-2-2222-22-2-2222i2i−2i−2i−2i−2i2i2i22-2-20000000000000000−2i2i2i−2i00000000000000000000000000000000
χ402222-2-2222-2-2-2-2-2-22-2-2-2222-22-2-222−2i−2i2i2i2i2i−2i−2i22-2-200000000000000002i−2i−2i2i00000000000000000000000000000000
χ4122-2-2222-2-222-2-2-2-2222-22-2-2-2200002i−2i2i−2i2i−2i2i−2i0000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000002-22-200000000
χ4222-2-2222-2-222-2-2-2-2222-22-2-2-2200002i−2i2i−2i2i−2i2i−2i000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000-22-2200000000
χ4322-2-2222-2-222-2-2-2-2222-22-2-2-220000−2i2i−2i2i−2i2i−2i2i0000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000-22-2200000000
χ4422-2-2222-2-222-2-2-2-2222-22-2-2-220000−2i2i−2i2i−2i2i−2i2i000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000002-22-200000000
χ4522-2-2222-2-222-2-2-2-22-2-22-2222-200002i−2i−2i2i2i−2i−2i2i000022-2-222-2-200000000000000000000000000002i−2i2i−2i000000000000
χ4622-2-2222-2-222-2-2-2-22-2-22-2222-200002i−2i−2i2i2i−2i−2i2i0000-2-222-2-2220000000000000000000000000000−2i2i−2i2i000000000000
χ4722-2-2222-2-222-2-2-2-22-2-22-2222-20000−2i2i2i−2i−2i2i2i−2i000022-2-222-2-20000000000000000000000000000−2i2i−2i2i000000000000
χ4822-2-2222-2-222-2-2-2-22-2-22-2222-20000−2i2i2i−2i−2i2i2i−2i0000-2-222-2-22200000000000000000000000000002i−2i2i−2i000000000000
χ4922-2-2-2-22-2-2-2-22222222-2-222-2-200002-22-2-22-220000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000−2i2i2i−2i00000000
χ5022-2-2-2-22-2-2-2-22222222-2-222-2-200002-22-2-22-22000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000002i−2i−2i2i00000000
χ5122-2-2-2-22-2-2-2-22222222-2-222-2-20000-22-222-22-20000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000002i−2i−2i2i00000000
χ5222-2-2-2-22-2-2-2-22222222-2-222-2-20000-22-222-22-2000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000−2i2i2i−2i00000000
χ5322-2-2-2-22-2-2-2-222222-2-222-2-22200002-2-22-222-2000022-2-2-2-22200000000000000000000000000002-2-22000000000000
χ5422-2-2-2-22-2-2-2-222222-2-222-2-22200002-2-22-222-20000-2-22222-2-20000000000000000000000000000-222-2000000000000
χ5522-2-2-2-22-2-2-2-222222-2-222-2-2220000-222-22-2-22000022-2-2-2-2220000000000000000000000000000-222-2000000000000
χ5622-2-2-2-22-2-2-2-222222-2-222-2-2220000-222-22-2-220000-2-22222-2-200000000000000000000000000002-2-22000000000000
χ572-22-222-22-2-2-222-2-222-22-22-2-222-22-2000000002-22-200000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ582-22-222-22-2-2-222-2-222-22-22-2-222-22-2000000002-22-20000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ592-22-222-22-2-2-222-2-222-22-22-2-22-22-2200000000-22-2200000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ602-22-222-22-2-2-222-2-222-22-22-2-22-22-2200000000-22-220000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ612-22-222-22-2-2-222-2-22-22-22-222-22-22-200000000-22-22000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ622-22-222-22-2-2-222-2-22-22-22-222-22-22-200000000-22-2200000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ632-22-222-22-2-2-222-2-22-22-22-222-2-22-22000000002-22-2000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ642-22-222-22-2-2-222-2-22-22-22-222-2-22-22000000002-22-200000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ652-22-2-2-2-22-222-2-22222-222-22-2-22-2-22000000002-2-2200000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ662-22-2-2-2-22-222-2-22222-222-22-2-22-2-22000000002-2-220000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ672-22-2-2-2-22-222-2-22222-222-22-2-2-222-200000000-222-200000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ682-22-2-2-2-22-222-2-22222-222-22-2-2-222-200000000-222-20000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ692-22-2-2-2-22-222-2-2222-22-2-22-2222-2-2200000000-222-2000000000000000000002-2-222-2-22000000000000000000000000
χ702-22-2-2-2-22-222-2-2222-22-2-22-2222-2-2200000000-222-200000000000000000000-222-2-222-2000000000000000000000000
χ712-22-2-2-2-22-222-2-2222-22-2-22-222-222-2000000002-2-22000000000000000000002-2-22-222-2000000000000000000000000
χ722-22-2-2-2-22-222-2-2222-22-2-22-222-222-2000000002-2-2200000000000000000000-222-22-2-22000000000000000000000000
χ7344444-4-4-4-44-44-44-4-40000000000000000000000000000000022−2222−2222−2222−22000000000000000000000000000000000000
χ7444444-4-4-4-44-44-44-4-400000000000000000000000000000000−2222−2222−2222−2222000000000000000000000000000000000000
χ754444-44-4-4-4-44-44-44-40000000000000000000000000000000022−2222−22−2222−2222000000000000000000000000000000000000
χ764444-44-4-4-4-44-44-44-400000000000000000000000000000000−2222−222222−2222−22000000000000000000000000000000000000
χ7744-4-44-4-4444-4-44-44-4000000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000
χ7844-4-44-4-4444-4-44-44-400000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000
χ7944-4-4-44-444-444-44-4-4000000000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000
χ8044-4-4-44-444-444-44-4-400000000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000
χ814-44-44-44-44-444-4-44-40000000000000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000000000000000
χ824-44-44-44-44-444-4-44-4000000000000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000000000000000
χ834-44-4-444-444-4-444-4-40000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000000000
χ844-44-4-444-444-4-444-4-4000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000000000
χ854-4-4444-4-44-4-4-4-44444-4-4-4-444400000000000000000000000000000000000000000000000000000000000000000000
χ864-4-4444-4-44-4-4-4-4444-44444-4-4-400000000000000000000000000000000000000000000000000000000000000000000
χ874-4-444-444-4-44-444-4-40000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ884-4-444-444-4-44-444-4-4000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ894-4-44-4444-44-44-4-44-40000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ904-4-44-4444-44-44-4-44-4000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ914-4-44-4-4-4-444444-4-444-4-444-44-400000000000000000000000000000000000000000000000000000000000000000000
χ924-4-44-4-4-4-444444-4-44-444-4-44-4400000000000000000000000000000000000000000000000000000000000000000000

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