Finite Group Databasebeta

← Group #379939

Character table — Group #379939

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222222222224444444444444444222244444444444444444444444444444444888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ711111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ811111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ91111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ101111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ121111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ141111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ151111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ161111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ17111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i1-11-11-11-1
χ18111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii-11-11-11-11
χ19111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i-11-11-11-11
χ20111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii1-11-11-11-1
χ21111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111ii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii1-1-11-111-1
χ22111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i-111-11-1-11
χ23111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii-111-11-1-11
χ24111-1-1-1-11111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i1-1-11-111-1
χ25111-1-1-1-11111-1-1-1-11-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii1-11-1-11-11
χ26111-1-1-1-11111-1-1-1-11-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i-11-111-11-1
χ27111-1-1-1-11111-1-1-1-11-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii-11-111-11-1
χ28111-1-1-1-11111-1-1-1-11-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i1-11-1-11-11
χ29111-1-1-1-11111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i1-1-111-1-11
χ30111-1-1-1-11111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-111-1-111-1
χ31111-1-1-1-11111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-111-1-111-1
χ32111-1-1-1-11111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii1-1-111-1-11
χ33222222222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222-2-2-2-2-2-20000000000000000000000000000000000000000
χ34222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22222220000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-222-2-222-2-2-2-20000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-222-2-222220000000000000000000000000000000000000000
χ37222-2-2-2-22222-2-2-2-222222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-222-2-2220000000000000000000000000000000000000000
χ38222-2-2-2-22222-2-2-2-222222-2-2-2-2-2-2-2-22222-2-222-2-222-2-22222-2-222-2-20000000000000000000000000000000000000000
χ39222-2-2-2-22222-2-2-2-22-2-2-2-22222-2-2-2-2222222-2-222-2-2-2-22222-2-2-2-2220000000000000000000000000000000000000000
χ40222-2-2-2-22222-2-2-2-22-2-2-2-22222-2-2-2-22222-2-22222-2-222-2-2-2-22222-2-20000000000000000000000000000000000000000
χ4122-222-2-222-2-222-2-2-22i2i−2i−2i2i2i−2i−2i000000002-22-200002i−2i002i−2i00000000000000000000002−22−2i2−i2i2−i22−22−2i2−i2i2−i200000000
χ4222-222-2-222-2-222-2-2-22i2i−2i−2i2i2i−2i−2i000000002-22-200002i−2i002i−2i0000000000000000000000−22−22−i2i2−i2i2−22−22−i2i2−i2i200000000
χ4322-222-2-222-2-222-2-2-22i2i−2i−2i2i2i−2i−2i00000000-22-220000−2i2i00−2i2i00000000000000000000002−22−2i2−i2i2−i2−22−22−i2i2−i2i200000000
χ4422-222-2-222-2-222-2-2-22i2i−2i−2i2i2i−2i−2i00000000-22-220000−2i2i00−2i2i0000000000000000000000−22−22−i2i2−i2i22−22−2i2−i2i2−i200000000
χ4522-222-2-222-2-222-2-2-2−2i−2i2i2i−2i−2i2i2i000000002-22-20000−2i2i00−2i2i00000000000000000000002−22−2−i2i2−i2i22−22−2−i2i2−i2i200000000
χ4622-222-2-222-2-222-2-2-2−2i−2i2i2i−2i−2i2i2i000000002-22-20000−2i2i00−2i2i0000000000000000000000−22−22i2−i2i2−i2−22−22i2−i2i2−i200000000
χ4722-222-2-222-2-222-2-2-2−2i−2i2i2i−2i−2i2i2i00000000-22-2200002i−2i002i−2i00000000000000000000002−22−2−i2i2−i2i2−22−22i2−i2i2−i200000000
χ4822-222-2-222-2-222-2-2-2−2i−2i2i2i−2i−2i2i2i00000000-22-2200002i−2i002i−2i0000000000000000000000−22−22i2−i2i2−i22−22−2−i2i2−i2i200000000
χ4922-2-2-22222-2-2-2-222-22i2i−2i−2i−2i−2i2i2i000000002-2-2200002i−2i00−2i2i0000000000000000000000i2−i2−i2i2−222−2i2−i2−i2i2−222−200000000
χ5022-2-2-22222-2-2-2-222-22i2i−2i−2i−2i−2i2i2i000000002-2-2200002i−2i00−2i2i0000000000000000000000−i2i2i2−i22−2−22−i2i2i2−i22−2−2200000000
χ5122-2-2-22222-2-2-2-222-22i2i−2i−2i−2i−2i2i2i00000000-222-20000−2i2i002i−2i0000000000000000000000i2−i2−i2i2−222−2−i2i2i2−i22−2−2200000000
χ5222-2-2-22222-2-2-2-222-22i2i−2i−2i−2i−2i2i2i00000000-222-20000−2i2i002i−2i0000000000000000000000−i2i2i2−i22−2−22i2−i2−i2i2−222−200000000
χ5322-2-2-22222-2-2-2-222-2−2i−2i2i2i2i2i−2i−2i000000002-2-220000−2i2i002i−2i0000000000000000000000i2−i2−i2i22−2−22i2−i2−i2i22−2−2200000000
χ5422-2-2-22222-2-2-2-222-2−2i−2i2i2i2i2i−2i−2i000000002-2-220000−2i2i002i−2i0000000000000000000000−i2i2i2−i2−222−2−i2i2i2−i2−222−200000000
χ5522-2-2-22222-2-2-2-222-2−2i−2i2i2i2i2i−2i−2i00000000-222-200002i−2i00−2i2i0000000000000000000000i2−i2−i2i22−2−22−i2i2i2−i2−222−200000000
χ5622-2-2-22222-2-2-2-222-2−2i−2i2i2i2i2i−2i−2i00000000-222-200002i−2i00−2i2i0000000000000000000000−i2i2i2−i2−222−2i2−i2−i2i22−2−2200000000
χ572-2-222222-22-2-2-2-2-222-22-22-22-222-2-22-22-200002-22-2000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ582-2-222222-22-2-2-2-2-222-22-22-22-222-2-22-22-200002-22-200000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ592-2-222222-22-2-2-2-2-222-22-22-22-2-2-222-22-220000-22-220000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ602-2-222222-22-2-2-2-2-222-22-22-22-2-2-222-22-220000-22-22000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ612-2-222222-22-2-2-2-2-22-22-22-22-2222-2-22-22-20000-22-22000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ622-2-222222-22-2-2-2-2-22-22-22-22-2222-2-22-22-20000-22-2200000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ632-2-222222-22-2-2-2-2-22-22-22-22-22-2-222-22-2200002-22-20000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ642-2-222222-22-2-2-2-2-22-22-22-22-22-2-222-22-2200002-22-2000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ652-2-2-2-2-2-22-22-2222222-22-2-22-2222-2-2-22-2200002-2-22000000000000000000002-2-222-2-22000000000000000000000000
χ662-2-2-2-2-2-22-22-2222222-22-2-22-2222-2-2-22-2200002-2-2200000000000000000000-222-2-222-2000000000000000000000000
χ672-2-2-2-2-2-22-22-2222222-22-2-22-22-2-2222-22-20000-222-20000000000002-2-222-2-2200000000000000000000000000000000
χ682-2-2-2-2-2-22-22-2222222-22-2-22-22-2-2222-22-20000-222-2000000000000-222-2-222-200000000000000000000000000000000
χ692-2-2-2-2-2-22-22-222222-22-222-22-222-2-2-22-220000-222-2000000000000000000002-2-22-222-2000000000000000000000000
χ702-2-2-2-2-2-22-22-222222-22-222-22-222-2-2-22-220000-222-200000000000000000000-222-22-2-22000000000000000000000000
χ712-2-2-2-2-2-22-22-222222-22-222-22-2-2-2222-22-200002-2-220000000000002-2-22-222-200000000000000000000000000000000
χ722-2-2-2-2-2-22-22-222222-22-222-22-2-2-2222-22-200002-2-22000000000000-222-22-2-2200000000000000000000000000000000
χ734444-44-4-4-4-4-44-44-44000000004-44-444-4-4000000000000000000000000000000000000000000000000000000000000
χ744444-44-4-4-4-4-44-44-4400000000-44-44-4-444000000000000000000000000000000000000000000000000000000000000
χ75444-44-44-4-4-4-4-44-444000000004-44-4-4-444000000000000000000000000000000000000000000000000000000000000
χ76444-44-44-4-4-4-4-44-44400000000-44-4444-4-4000000000000000000000000000000000000000000000000000000000000
χ7744-44-4-44-4-4444-4-44-4000000000000000000000000000000004i−4i4i−4i0000000000000000000000000000000000000000
χ7844-44-4-44-4-4444-4-44-400000000000000000000000000000000−4i4i−4i4i0000000000000000000000000000000000000000
χ7944-4-444-4-4-444-444-4-4000000000000000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ8044-4-444-4-4-444-444-4-400000000000000000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ814-4444-4-44-4-44-4-444-44i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ824-4444-4-44-4-44-4-444-4−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ834-444-4-44-444-4-444-4-4000000000000000000000000004i−4i004i−4i00000000000000000000000000000000000000000000
χ844-444-4-44-444-4-444-4-400000000000000000000000000−4i4i00−4i4i00000000000000000000000000000000000000000000
χ854-44-444-4-444-44-4-44-4000000000000000000000000004i−4i00−4i4i00000000000000000000000000000000000000000000
χ864-44-444-4-444-44-4-44-400000000000000000000000000−4i4i004i−4i00000000000000000000000000000000000000000000
χ874-44-4-4444-4-4444-4-4-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ884-44-4-4444-4-4444-4-4-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ894-4-44-44-4-44-44-44-444000000004-4-444-4-44000000000000000000000000000000000000000000000000000000000000
χ904-4-44-44-4-44-44-44-44400000000-444-4-444-4000000000000000000000000000000000000000000000000000000000000
χ914-4-4-44-44-44-444-44-44000000004-4-44-444-4000000000000000000000000000000000000000000000000000000000000
χ924-4-4-44-44-44-444-44-4400000000-444-44-4-44000000000000000000000000000000000000000000000000000000000000

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