Finite Group Databasebeta

← Group #119708

Character table — Group #119708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222444444442222444444444444444444444444444444442222444444444444888888888888888844448888
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
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-111-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-111-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii
χ1722222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ1822222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ192222222222222222-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000022-2-2-2-22200000000000000000000000000000000
χ202222222222222222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000-2-22222-2-200000000000000000000000000000000
χ212222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ2322222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2-2-22200000000000000002222-2-2-2-200000000000000000000000000000000
χ2422222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-222-2-2-2-2220000000000000000-2-2-2-2222200000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-222-2-2-2-2-2-22222-2-200000000000000000000000022-2-2-2-222000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-222-2-2-2-2-2-22222-2-2000000000000000000000000-2-22222-2-2000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-222-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-222-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000
χ29222-2-2-2-222222-2-2-2-2-22-22000022-2-200000000000022-2-2000022-2-20000000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000
χ30222-2-2-2-222222-2-2-2-2-22-22000022-2-200000000000022-2-2000022-2-20000000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000
χ31222-2-2-2-222222-2-2-2-2-22-22000022-2-2000000000000-2-2220000-2-2220000000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000
χ32222-2-2-2-222222-2-2-2-2-22-22000022-2-2000000000000-2-2220000-2-2220000000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000
χ33222-2-2-2-22-2-2-2-222222-22-2000022-2-20000000000002i2i−2i−2i0000−2i−2i2i2i0000000000000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−200000000
χ34222-2-2-2-22-2-2-2-222222-22-2000022-2-20000000000002i2i−2i−2i0000−2i−2i2i2i0000000000000000−i2−i2i2i2i2i2−i2−i222−2−2−2−22200000000
χ35222-2-2-2-22-2-2-2-222222-22-2000022-2-2000000000000−2i−2i2i2i00002i2i−2i−2i0000000000000000i2i2−i2−i2−i2−i2i2i222−2−2−2−22200000000
χ36222-2-2-2-22-2-2-2-222222-22-2000022-2-2000000000000−2i−2i2i2i00002i2i−2i−2i0000000000000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−200000000
χ3722-22-22-2-22i2i−2i−2i2i−2i2i−2i00002-22i−2i00002-22i−2i00001+i1+i−1−i−1−i1+i−1−i1+i−1−i1−i1−i−1+i−1+i1−i−1+i1−i−1+i002-22i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000
χ3822-22-22-2-22i2i−2i−2i2i−2i2i−2i00002-22i−2i00002-22i−2i00001+i1+i−1−i−1−i1+i−1−i1+i−1−i1−i1−i−1+i−1+i1−i−1+i1−i−1+i00-22−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000
χ3922-22-22-2-22i2i−2i−2i2i−2i2i−2i00002-22i−2i00002-22i−2i0000−1−i−1−i1+i1+i−1−i1+i−1−i1+i−1+i−1+i1−i1−i−1+i1−i−1+i1−i002-22i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000
χ4022-22-22-2-22i2i−2i−2i2i−2i2i−2i00002-22i−2i00002-22i−2i0000−1−i−1−i1+i1+i−1−i1+i−1−i1+i−1+i−1+i1−i1−i−1+i1−i−1+i1−i00-22−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000
χ4122-22-22-2-22i2i−2i−2i2i−2i2i−2i0000-22−2i2i0000-22−2i2i00001+i1+i−1−i−1−i−1−i1+i−1−i1+i1−i1−i−1+i−1+i−1+i1−i−1+i1−i2-200002i−2i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000000000000000
χ4222-22-22-2-22i2i−2i−2i2i−2i2i−2i0000-22−2i2i0000-22−2i2i00001+i1+i−1−i−1−i−1−i1+i−1−i1+i1−i1−i−1+i−1+i−1+i1−i−1+i1−i-220000−2i2i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000000000000000
χ4322-22-22-2-22i2i−2i−2i2i−2i2i−2i0000-22−2i2i0000-22−2i2i0000−1−i−1−i1+i1+i1+i−1−i1+i−1−i−1+i−1+i1−i1−i1−i−1+i1−i−1+i2-200002i−2i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000000000000000
χ4422-22-22-2-22i2i−2i−2i2i−2i2i−2i0000-22−2i2i0000-22−2i2i0000−1−i−1−i1+i1+i1+i−1−i1+i−1−i−1+i−1+i1−i1−i1−i−1+i1−i−1+i-220000−2i2i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000000000000000
χ4522-22-22-2-2−2i−2i2i2i−2i2i−2i2i00002-2−2i2i00002-2−2i2i00001−i1−i−1+i−1+i1−i−1+i1−i−1+i1+i1+i−1−i−1−i1+i−1−i1+i−1−i002-2−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000
χ4622-22-22-2-2−2i−2i2i2i−2i2i−2i2i00002-2−2i2i00002-2−2i2i00001−i1−i−1+i−1+i1−i−1+i1−i−1+i1+i1+i−1−i−1−i1+i−1−i1+i−1−i00-222i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000000000
χ4722-22-22-2-2−2i−2i2i2i−2i2i−2i2i00002-2−2i2i00002-2−2i2i0000−1+i−1+i1−i1−i−1+i1−i−1+i1−i−1−i−1−i1+i1+i−1−i1+i−1−i1+i002-2−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000000000
χ4822-22-22-2-2−2i−2i2i2i−2i2i−2i2i00002-2−2i2i00002-2−2i2i0000−1+i−1+i1−i1−i−1+i1−i−1+i1−i−1−i−1−i1+i1+i−1−i1+i−1−i1+i00-222i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000
χ4922-22-22-2-2−2i−2i2i2i−2i2i−2i2i0000-222i−2i0000-222i−2i00001−i1−i−1+i−1+i−1+i1−i−1+i1−i1+i1+i−1−i−1−i−1−i1+i−1−i1+i2-20000−2i2i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000000000000000
χ5022-22-22-2-2−2i−2i2i2i−2i2i−2i2i0000-222i−2i0000-222i−2i00001−i1−i−1+i−1+i−1+i1−i−1+i1−i1+i1+i−1−i−1−i−1−i1+i−1−i1+i-2200002i−2i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000000000000000
χ5122-22-22-2-2−2i−2i2i2i−2i2i−2i2i0000-222i−2i0000-222i−2i0000−1+i−1+i1−i1−i1−i−1+i1−i−1+i−1−i−1−i1+i1+i1+i−1−i1+i−1−i2-20000−2i2i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000000000000000
χ5222-22-22-2-2−2i−2i2i2i−2i2i−2i2i0000-222i−2i0000-222i−2i0000−1+i−1+i1−i1−i1−i−1+i1−i−1+i−1−i−1−i1+i1+i1+i−1−i1+i−1−i-2200002i−2i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000000000000000
χ532-2-222-2-222-22-222-2-22-2-2222-2-22-22-2-2-2222-22-2000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ542-2-222-2-222-22-222-2-22-2-2222-2-22-22-2-2-2222-22-200000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ552-2-222-2-222-22-222-2-22-2-22-2-2222-22-222-2-2-22-2200000000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000
χ562-2-222-2-222-22-222-2-22-2-22-2-2222-22-222-2-2-22-220000000000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ572-2-222-2-222-22-222-2-2-222-222-2-2-22-22-2-222-22-220000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ582-2-222-2-222-22-222-2-2-222-222-2-2-22-22-2-222-22-22000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ592-2-222-2-222-22-222-2-2-222-2-2-222-22-2222-2-22-22-200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ602-2-222-2-222-22-222-2-2-222-2-2-222-22-2222-2-22-22-20000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ612-2-222-2-22-22-22-2-2222-2-222222-22-22-2-2-2-2-222-20000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ622-2-222-2-22-22-22-2-2222-2-222222-22-22-2-2-2-2-222-2000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ632-2-222-2-22-22-22-2-2222-2-22-2-2-2-2-22-2222222-2-2200000000000000000000000000000000000000000000000000002-2-22
χ642-2-222-2-22-22-22-2-2222-2-22-2-2-2-2-22-2222222-2-220000000000000000000000000000000000000000000000000000-222-2
χ652-2-222-2-22-22-22-2-222-222-222222-22-2-2-2-2-22-2-22000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ662-2-222-2-22-22-22-2-222-222-222222-22-2-2-2-2-22-2-2200000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ672-2-222-2-22-22-22-2-222-222-2-2-2-2-22-22-22222-222-200000000000000000000000000000000000000002-22-2-22-2200000000
χ682-2-222-2-22-22-22-2-222-222-2-2-2-2-22-22-22222-222-20000000000000000000000000000000000000000-22-222-22-200000000
χ692-2-2-2-22222-22-2-2-222-2-22200002-2-22000000002-22-200002-22-2000000000000000000002−2−222−2−222−2−222−2−2200000000
χ702-2-2-2-22222-22-2-2-222-2-22200002-2-22000000002-22-200002-22-200000000000000000000−222−2−222−2−222−2−222−200000000
χ712-2-2-2-22222-22-2-2-222-2-22200002-2-2200000000-22-220000-22-22000000000000000000002−2−222−2−22−222−2−222−200000000
χ722-2-2-2-22222-22-2-2-222-2-22200002-2-2200000000-22-220000-22-2200000000000000000000−222−2−222−22−2−222−2−2200000000
χ732-2-2-2-2222-22-2222-2-222-2-200002-2-22000000002i−2i2i−2i0000−2i2i−2i2i000000000000000000002−2−22−222−2i2−i2−i2i2−i2i2i2−i200000000
χ742-2-2-2-2222-22-2222-2-222-2-200002-2-22000000002i−2i2i−2i0000−2i2i−2i2i00000000000000000000−222−22−2−22−i2i2i2−i2i2−i2−i2i200000000
χ752-2-2-2-2222-22-2222-2-222-2-200002-2-2200000000−2i2i−2i2i00002i−2i2i−2i000000000000000000002−2−22−222−2−i2i2i2−i2i2−i2−i2i200000000
χ762-2-2-2-2222-22-2222-2-222-2-200002-2-2200000000−2i2i−2i2i00002i−2i2i−2i00000000000000000000−222−22−2−22i2−i2−i2i2−i2i2i2−i200000000
χ77444-4-4-4-444444-4-4-4-44-44-40000-4-4440000000000000000000000000000000000000000000000000000000000000000
χ78444-4-4-4-44-4-4-4-44444-44-440000-4-4440000000000000000000000000000000000000000000000000000000000000000
χ7944-4-44-44-44i4i−4i−4i−4i4i−4i4i0000000000000000000000002+2i−2−2i−2−2i2+2i00002−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000000
χ8044-4-44-44-44i4i−4i−4i−4i4i−4i4i000000000000000000000000−2−2i2+2i2+2i−2−2i0000−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000000
χ8144-4-44-44-4−4i−4i4i4i4i−4i4i−4i0000000000000000000000002−2i−2+2i−2+2i2−2i00002+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000000
χ8244-4-44-44-4−4i−4i4i4i4i−4i4i−4i000000000000000000000000−2+2i2−2i2−2i−2+2i0000−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000000
χ834-444-4-44-44i−4i−4i4i4i−4i−4i4i00004-4−4i4i0000-444i−4i000000000000000000000000000000000000000000000000000000000000
χ844-444-4-44-44i−4i−4i4i4i−4i−4i4i0000-444i−4i00004-4−4i4i000000000000000000000000000000000000000000000000000000000000
χ854-444-4-44-4−4i4i4i−4i−4i4i4i−4i00004-44i−4i0000-44−4i4i000000000000000000000000000000000000000000000000000000000000
χ864-444-4-44-4−4i4i4i−4i−4i4i4i−4i0000-44−4i4i00004-44i−4i000000000000000000000000000000000000000000000000000000000000
χ874-44-444-4-44i−4i−4i4i−4i4i4i−4i000000000000000000002+2i−2−2i−2−2i2+2i00002−2i−2+2i−2+2i2−2i00000000000000000000000000000000000000000000
χ884-44-444-4-44i−4i−4i4i−4i4i4i−4i00000000000000000000−2−2i2+2i2+2i−2−2i0000−2+2i2−2i2−2i−2+2i00000000000000000000000000000000000000000000
χ894-44-444-4-4−4i4i4i−4i4i−4i−4i4i000000000000000000002−2i−2+2i−2+2i2−2i00002+2i−2−2i−2−2i2+2i00000000000000000000000000000000000000000000
χ904-44-444-4-4−4i4i4i−4i4i−4i−4i4i00000000000000000000−2+2i2−2i2−2i−2+2i0000−2−2i2+2i2+2i−2−2i00000000000000000000000000000000000000000000
χ914-4-4-4-44444-44-4-4-44444-4-40000-444-40000000000000000000000000000000000000000000000000000000000000000
χ924-4-4-4-4444-44-4444-4-4-4-4440000-444-40000000000000000000000000000000000000000000000000000000000000000

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