Finite Group Databasebeta

← Group #481521

Character table — Group #481521

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111111122222222222244444444444444448888888888888888888888888888888888881616161616161616
order12224444224444444444222244444444444424444444444444444444888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1
χ91111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-111-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-1
χ101111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-111-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-111
χ111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-111-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-11-1-111
χ121111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-111-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111-11-111-1-1
χ131111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-111-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-11-1-1-111
χ141111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-111-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-11-1111-1-1
χ151111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-111-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-11-1111-1-1
χ161111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-111-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-11-1-1-111
χ171111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i1-1-111-11-1
χ181111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii-111-1-11-11
χ191111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i-111-1-11-11
χ201111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii1-1-111-11-1
χ211111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-1111-1-11-11-11
χ221111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-111-1-111-1-1-1-111-1-111-1-111-1-11111-1-111-1-1-111-11-11-1
χ231111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111-1-11111-1-111-1-111-1-111-1-1-1-111-1-111-111-11-11-1
χ241111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-111-1-11-1-11-11-11
χ251111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-11-11ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii11-1-11-1-11
χ261111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-11-11ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i-1-111-111-1
χ271111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-11-11−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii-1-111-111-1
χ281111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-11-11−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i11-1-11-1-11
χ291111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-11-1111-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-111-1
χ301111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-11-1111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111-1-1111-1-11
χ311111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-11-11-1-11111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1111-1-11
χ321111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-11-11-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-111-1
χ332222222222222222222222-2-222-2-222-2-2-2-222-2-2-2-20000000000000000000000000000000000000000
χ3422222222222222222222-2-222-2-222-2-22222-2-2-2-2-2-20000000000000000000000000000000000000000
χ352222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222-2-2222-2-220000000000000000000000000000000000000000
χ362222222222-2-2-2-2-2-2-2-222-2-22222-2-222-2-222-2-22-2-220000000000000000000000000000000000000000
χ372222-2-2-2-2222222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-2-2-2220000000000000000000000000000000000000000
χ382222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2220000000000000000000000000000000000000000
χ392222-2-2-2-222-2-2-2-22222-2-22222-2-22222-2-2-2-2-2-22-22-20000000000000000000000000000000000000000
χ402222-2-2-2-222-2-2-2-22222-2-2-2-2-2-222-2-2-2-22222222-22-20000000000000000000000000000000000000000
χ4122-2-22i2i−2i−2i2-22i2i−2i−2i22-2-22i−2i002-2002-2002i−2i2i−2i00000000000000000000002−2i2−i2i2−i22−2i2−i22−22−2i2−i200000000
χ4222-2-22i2i−2i−2i2-22i2i−2i−2i22-2-22i−2i002-2002-2002i−2i2i−2i0000000000000000000000−22−i2i2−i2i2−22−i2i2−22−22−i2i200000000
χ4322-2-22i2i−2i−2i2-22i2i−2i−2i22-2-22i−2i00-2200-2200−2i2i−2i2i0000000000000000000000i2−i2−22−22i2−i22−2−i2i2−i2i22−200000000
χ4422-2-22i2i−2i−2i2-22i2i−2i−2i22-2-22i−2i00-2200-2200−2i2i−2i2i0000000000000000000000−i2i22−22−2−i2i2−22i2−i2i2−i2−2200000000
χ4522-2-22i2i−2i−2i2-2−2i−2i2i2i-2-2222i−2i002-200-2200−2i2i2i−2i00000000000000000000002−2i2−i2−i2i2−22i2−i22−2−22−i2i200000000
χ4622-2-22i2i−2i−2i2-2−2i−2i2i2i-2-2222i−2i002-200-2200−2i2i2i−2i0000000000000000000000−22−i2i2i2−i22−2−i2i2−222−2i2−i200000000
χ4722-2-22i2i−2i−2i2-2−2i−2i2i2i-2-2222i−2i00-22002-2002i−2i−2i2i0000000000000000000000i2−i2−222−2−i2i22−2−i2i2i2−i2−2200000000
χ4822-2-22i2i−2i−2i2-2−2i−2i2i2i-2-2222i−2i00-22002-2002i−2i−2i2i0000000000000000000000−i2i22−2−22i2−i2−22i2−i2−i2i22−200000000
χ4922-2-22i2i−2i−2i-222i−2i2i−2i2-22-2−2i2i2-2002i−2i002-200002i−2i00001+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000000000000000
χ5022-2-22i2i−2i−2i-222i−2i2i−2i2-22-2−2i2i2-2002i−2i002-200002i−2i0000−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000000000000000
χ5122-2-22i2i−2i−2i-222i−2i2i−2i2-22-2−2i2i-2200−2i2i00-220000−2i2i00001−i−1+i−1−i1+i−1−i1+i1−i−1+i−1+i1−i1+i−1−i1+i−1−i−1+i1−i000000000000000000000000
χ5222-2-22i2i−2i−2i-222i−2i2i−2i2-22-2−2i2i-2200−2i2i00-220000−2i2i0000−1+i1−i1+i−1−i1+i−1−i−1+i1−i1−i−1+i−1−i1+i−1−i1+i1−i−1+i000000000000000000000000
χ5322-2-22i2i−2i−2i-22−2i2i−2i2i-22-22−2i2i2-200−2i2i00-2200002i−2i00001+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i000000000000000000000000
χ5422-2-22i2i−2i−2i-22−2i2i−2i2i-22-22−2i2i2-200−2i2i00-2200002i−2i0000−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i000000000000000000000000
χ5522-2-22i2i−2i−2i-22−2i2i−2i2i-22-22−2i2i-22002i−2i002-20000−2i2i00001−i−1+i−1−i1+i1+i−1−i−1+i1−i−1+i1−i1+i−1−i−1−i1+i1−i−1+i000000000000000000000000
χ5622-2-22i2i−2i−2i-22−2i2i−2i2i-22-22−2i2i-22002i−2i002-20000−2i2i0000−1+i1−i1+i−1−i−1−i1+i1−i−1+i1−i−1+i−1−i1+i1+i−1−i−1+i1−i000000000000000000000000
χ5722-2-2−2i−2i2i2i2-22i2i−2i−2i-2-222−2i2i002-200-22002i−2i−2i2i00000000000000000000002−2−i2i2i2−i2−22−i2i22−2−22i2−i200000000
χ5822-2-2−2i−2i2i2i2-22i2i−2i−2i-2-222−2i2i002-200-22002i−2i−2i2i0000000000000000000000−22i2−i2−i2i22−2i2−i2−222−2−i2i200000000
χ5922-2-2−2i−2i2i2i2-22i2i−2i−2i-2-222−2i2i00-22002-200−2i2i2i−2i0000000000000000000000i2−i22−2−22−i2i2−22−i2i2i2−i22−200000000
χ6022-2-2−2i−2i2i2i2-22i2i−2i−2i-2-222−2i2i00-22002-200−2i2i2i−2i0000000000000000000000−i2i2−222−2i2−i22−2i2−i2−i2i2−2200000000
χ6122-2-2−2i−2i2i2i2-2−2i−2i2i2i22-2-2−2i2i002-2002-200−2i2i−2i2i00000000000000000000002−2−i2i2−i2i22−2−i2i22−22−2−i2i200000000
χ6222-2-2−2i−2i2i2i2-2−2i−2i2i2i22-2-2−2i2i002-2002-200−2i2i−2i2i0000000000000000000000−22i2−i2i2−i2−22i2−i2−22−22i2−i200000000
χ6322-2-2−2i−2i2i2i2-2−2i−2i2i2i22-2-2−2i2i00-2200-22002i−2i2i−2i0000000000000000000000i2−i22−22−2i2−i2−22−i2i2−i2i2−2200000000
χ6422-2-2−2i−2i2i2i2-2−2i−2i2i2i22-2-2−2i2i00-2200-22002i−2i2i−2i0000000000000000000000−i2i2−22−22−i2i22−2i2−i2i2−i22−200000000
χ6522-2-2−2i−2i2i2i-222i−2i2i−2i-22-222i−2i2-2002i−2i00-220000−2i2i00001−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i000000000000000000000000
χ6622-2-2−2i−2i2i2i-222i−2i2i−2i-22-222i−2i2-2002i−2i00-220000−2i2i0000−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i000000000000000000000000
χ6722-2-2−2i−2i2i2i-222i−2i2i−2i-22-222i−2i-2200−2i2i002-200002i−2i00001+i−1−i−1+i1−i1−i−1+i−1−i1+i−1−i1+i1−i−1+i−1+i1−i1+i−1−i000000000000000000000000
χ6822-2-2−2i−2i2i2i-222i−2i2i−2i-22-222i−2i-2200−2i2i002-200002i−2i0000−1−i1+i1−i−1+i−1+i1−i1+i−1−i1+i−1−i−1+i1−i1−i−1+i−1−i1+i000000000000000000000000
χ6922-2-2−2i−2i2i2i-22−2i2i−2i2i2-22-22i−2i2-200−2i2i002-20000−2i2i00001−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000000000000000
χ7022-2-2−2i−2i2i2i-22−2i2i−2i2i2-22-22i−2i2-200−2i2i002-20000−2i2i0000−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000000000000000
χ7122-2-2−2i−2i2i2i-22−2i2i−2i2i2-22-22i−2i-22002i−2i00-2200002i−2i00001+i−1−i−1+i1−i−1+i1−i1+i−1−i−1−i1+i1−i−1+i1−i−1+i−1−i1+i000000000000000000000000
χ7222-2-2−2i−2i2i2i-22−2i2i−2i2i2-22-22i−2i-22002i−2i00-2200002i−2i0000−1−i1+i1−i−1+i1−i−1+i−1−i1+i1+i−1−i−1+i1−i−1+i1−i1+i−1−i000000000000000000000000
χ7344444444-4-44-4-444-4-44-4-4000000000000000000000000000000000000000000000000000000000000
χ7444444444-4-4-444-4-444-4-4-4000000000000000000000000000000000000000000000000000000000000
χ754444-4-4-4-4-4-44-4-44-444-444000000000000000000000000000000000000000000000000000000000000
χ764444-4-4-4-4-4-4-444-44-4-4444000000000000000000000000000000000000000000000000000000000000
χ778-88-88i−8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000
χ788-88-8−8i8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000
χ798-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000000000
χ808-8-88-888-8000000000000000000000000000000000000000000000000000000000000000000000000

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