Finite Group Databasebeta

← Group #120607

Character table — Group #120607

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222222222224444444444444444444488888888888888884444444488888888888888888888888844444444
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
χ911111-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1-11111-111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i
χ1011111-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1-11111-111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−iii−i−iii
χ1111111-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1-11111-111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii
χ1211111-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1-11111-111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111ii−i−iii−i−i
χ1311111-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ1411111-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−iiiii−i−i
χ1511111-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ1611111-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1ii−i−i−i−iii
χ17222222222222222222-2-22222-2-2-2-2-222-2-2-2-2-2000000000000000022-2-222-2-200000000000000000000000000000000
χ18222222222222222222-2-22222-2-2-2-2-222-2-2-2-2-20000000000000000-2-222-2-22200000000000000000000000000000000
χ192222222222222222-2-222-2-2-2-222222-2-22-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ202222222222222222-2-222-2-2-2-222222-2-22-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
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
χ2322222-2-2-2-2-2222-2-2-222-2-2-2-2-2-2222-2-2222-2-22200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ2422222-2-2-2-2-2222-2-2-222-2-2-2-2-2-2222-2-2222-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ2522222-2-2-2-2-2222-2-2-2-2-2222222-2-2-222-2-2-2-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ2622222-2-2-2-2-2222-2-2-2-2-2222222-2-2-222-2-2-2-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ2722222-2-2-2-2-2222-2-2-2-2-2-2-22222222-2-2-2-2222-2-200000000000000000000000022-2-2-2-222000000000000000000000000
χ2822222-2-2-2-2-2222-2-2-2-2-2-2-22222222-2-2-2-2222-2-2000000000000000000000000-2-22222-2-2000000000000000000000000
χ29222-2-22222-22-2-2-2-2-2002-2000022-22-200-20000000022-2-2000022-2-2000000000000000022−2−222−2−222−2−222−2−200000000
χ30222-2-22222-22-2-2-2-2-2002-2000022-22-200-20000000022-2-2000022-2-20000000000000000−2−222−2−222−2−222−2−22200000000
χ31222-2-22222-22-2-2-2-2-2002-2000022-22-200-200000000-2-2220000-2-222000000000000000022−2−222−2−2−2−222−2−22200000000
χ32222-2-22222-22-2-2-2-2-2002-2000022-22-200-200000000-2-2220000-2-2220000000000000000−2−222−2−22222−2−222−2−200000000
χ33222-2-2-2-2-2-222-2-2222002-20000-2-222-20020000000022-2-20000-2-222000000000000000022−2−2−2−22222−2−2−2−22200000000
χ34222-2-2-2-2-2-222-2-2222002-20000-2-222-20020000000022-2-20000-2-2220000000000000000−2−22222−2−2−2−22222−2−200000000
χ35222-2-2-2-2-2-222-2-2222002-20000-2-222-200200000000-2-222000022-2-2000000000000000022−2−2−2−222−2−22222−2−200000000
χ36222-2-2-2-2-2-222-2-2222002-20000-2-222-200200000000-2-222000022-2-20000000000000000−2−22222−2−222−2−2−2−22200000000
χ3722-22-222-2-22-22-22-2-2220022-2-200000-2-20000022−2−22−22−222−2−22−22−2002-2002-22−22−22−22−2000000000000000000000000
χ3822-22-222-2-22-22-22-2-2220022-2-200000-2-20000022−2−22−22−222−2−22−22−200-2200-22−22−22−22−22000000000000000000000000
χ3922-22-222-2-22-22-22-2-2220022-2-200000-2-200000−2−222−22−22−2−222−22−22002-2002-2−22−22−22−22000000000000000000000000
χ4022-22-222-2-22-22-22-2-2220022-2-200000-2-200000−2−222−22−22−2−222−22−2200-2200-222−22−22−22−2000000000000000000000000
χ4122-22-222-2-22-22-22-2-2-2-200-2-22200000220000022−2−2−22−2222−2−2−22−222i−2i002i−2i00i2−i2−i2i2i2−i2−i2i2000000000000000000000000
χ4222-22-222-2-22-22-22-2-2-2-200-2-22200000220000022−2−2−22−2222−2−2−22−22−2i2i00−2i2i00−i2i2i2−i2−i2i2i2−i2000000000000000000000000
χ4322-22-222-2-22-22-22-2-2-2-200-2-222000002200000−2−2222−22−2−2−2222−22−22i−2i002i−2i00−i2i2i2−i2−i2i2i2−i2000000000000000000000000
χ4422-22-222-2-22-22-22-2-2-2-200-2-222000002200000−2−2222−22−2−2−2222−22−2−2i2i00−2i2i00i2−i2−i2i2i2−i2−i2i2000000000000000000000000
χ4522-22-2-2-222-2-22-2-2222200-2-22200000-2-20000022−2−22−22−2−2−222−22−22002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ4622-22-2-2-222-2-22-2-2222200-2-22200000-2-20000022−2−22−22−2−2−222−22−2200−2i2i002i−2i−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ4722-22-2-2-222-2-22-2-2222200-2-22200000-2-200000−2−222−22−2222−2−22−22−2002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ4822-22-2-2-222-2-22-2-2222200-2-22200000-2-200000−2−222−22−2222−2−22−22−200−2i2i002i−2ii2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ4922-22-2-2-222-2-22-2-222-2-20022-2-200000220000022−2−2−22−22−2−2222−22−22-200-22002−2−22−222−2000000000000000000000000
χ5022-22-2-2-222-2-22-2-222-2-20022-2-200000220000022−2−2−22−22−2−2222−22−2-22002-200−222−22−2−22000000000000000000000000
χ5122-22-2-2-222-2-22-2-222-2-20022-2-2000002200000−2−2222−22−222−2−2−22−222-200-2200−222−22−2−22000000000000000000000000
χ5222-22-2-2-222-2-22-2-222-2-20022-2-2000002200000−2−2222−22−222−2−2−22−22-22002-2002−2−22−222−2000000000000000000000000
χ532-2-2222-22-222-2-2-2-22002-200002-22-2200-200002-22-200002-22-200000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ542-2-2222-22-222-2-2-2-22002-200002-22-2200-200002-22-200002-22-200000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ552-2-2222-22-222-2-2-2-22002-200002-22-2200-20000-22-220000-22-2200000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ562-2-2222-22-222-2-2-2-22002-200002-22-2200-20000-22-220000-22-2200000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ572-2-222-22-22-22-2-222-2002-20000-22-2-2200200002-22-20000-22-2200000000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ582-2-222-22-22-22-2-222-2002-20000-22-2-2200200002-22-20000-22-2200000000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ592-2-222-22-22-22-2-222-2002-20000-22-2-220020000-22-2200002-22-200000000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ602-2-222-22-22-22-2-222-2002-20000-22-2-220020000-22-2200002-22-200000000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ612-2-2-2-22-22-2-222222-22-2222-22-22-2-2-2-22-222-22-200000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ622-2-2-2-22-22-2-222222-22-2222-22-22-2-2-2-22-222-22-20000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ632-2-2-2-22-22-2-222222-22-2-2-22-22-2-222222-2-2-22-2200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ642-2-2-2-22-22-2-222222-22-2-2-22-22-2-222222-2-2-22-220000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ652-2-2-2-22-22-2-222222-2-2222-22-222-2-2-2-2-222-22-22000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ662-2-2-2-22-22-2-222222-2-2222-22-222-2-2-2-2-222-22-2200000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ672-2-2-2-22-22-2-222222-2-22-2-2-22-22-22222-22-22-22-20000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ682-2-2-2-22-22-2-222222-2-22-2-2-22-22-22222-22-22-22-2000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ692-2-2-2-2-22-222222-2-222-222-22-22-222-2-22-2-22-2-2200000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ702-2-2-2-2-22-222222-2-222-222-22-22-222-2-22-2-22-2-220000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ712-2-2-2-2-22-222222-2-222-2-2-2-22-222-2-2222-22-222-200000000000000000000000000000000000000000000000000002-2-22
χ722-2-2-2-2-22-222222-2-222-2-2-2-22-222-2-2222-22-222-20000000000000000000000000000000000000000000000000000-222-2
χ732-2-2-2-2-22-222222-2-22-22222-22-2-222-2-2-22-2-222-2000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ742-2-2-2-2-22-222222-2-22-22222-22-2-222-2-2-22-2-222-200000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ752-2-2-2-2-22-222222-2-22-22-2-22-22-22-2-222-2222-2-220000000000000000000000000000000000000000000000002-2-220000
χ762-2-2-2-2-22-222222-2-22-22-2-22-22-22-2-222-2222-2-22000000000000000000000000000000000000000000000000-222-20000
χ77444-4-44444-44-4-4-4-4-400-440000-4-44-44004000000000000000000000000000000000000000000000000000000000000
χ78444-4-4-4-4-4-444-4-444400-44000044-4-4400-4000000000000000000000000000000000000000000000000000000000000
χ7944-4-4444-4-4-4-4-44-44400000000000000000000000022−22−2222000022−22−22220000000000000000000000000000000000000000
χ8044-4-4444-4-4-4-4-44-444000000000000000000000000−222222−220000−222222−220000000000000000000000000000000000000000
χ8144-4-44-4-4444-4-444-4-400000000000000000000000022−22−22220000−222222−220000000000000000000000000000000000000000
χ8244-4-44-4-4444-4-444-4-4000000000000000000000000−222222−22000022−22−22220000000000000000000000000000000000000000
χ834-444-44-4-444-4-44-44-40000000000000000000022−22−2222000022−22−222200000000000000000000000000000000000000000000
χ844-444-44-4-444-4-44-44-400000000000000000000−222222−220000−222222−2200000000000000000000000000000000000000000000
χ854-444-4-444-4-4-4-444-440000000000000000000022−22−22220000−222222−2200000000000000000000000000000000000000000000
χ864-444-4-444-4-4-4-444-4400000000000000000000−222222−22000022−22−222200000000000000000000000000000000000000000000
χ874-44-444-4-44-4-44-44-444-4004-4-4400000-440000000000000000000000000000000000000000000000000000000000000
χ884-44-444-4-44-4-44-44-44-4400-444-4000004-40000000000000000000000000000000000000000000000000000000000000
χ894-44-44-444-44-44-4-44-44-400-444-400000-440000000000000000000000000000000000000000000000000000000000000
χ904-44-44-444-44-44-4-44-4-44004-4-44000004-40000000000000000000000000000000000000000000000000000000000000
χ914-4-4444-44-444-4-4-4-4400-440000-44-44-4004000000000000000000000000000000000000000000000000000000000000
χ924-4-444-44-44-44-4-444-400-4400004-444-400-4000000000000000000000000000000000000000000000000000000000000

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