Finite Group Databasebeta

← Group #120069

Character table — Group #120069

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222222222224444444444444444444488888888888888884444444444444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
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
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ911-1-1-1-1-111111-1-11-11111111-1-1-1-1-1-1-11-111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−i11-1-1
χ1011-1-1-1-1-111111-1-11-11111111-1-1-1-1-1-1-11-111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−iii-1-111
χ1111-1-1-1-1-111111-1-11-11111111-1-1-1-1-1-1-11-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1−i−iii-1-111
χ1211-1-1-1-1-111111-1-11-11111111-1-1-1-1-1-1-11-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−i11-1-1
χ1311-1-1-1-1-111111-1-11-11111111-1-1-1-1-1-1-11-111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i-1-111
χ1411-1-1-1-1-111111-1-11-11111111-1-1-1-1-1-1-11-111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii11-1-1
χ1511-1-1-1-1-111111-1-11-11111111-1-1-1-1-1-1-11-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii11-1-1
χ1611-1-1-1-1-111111-1-11-11111111-1-1-1-1-1-1-11-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1ii−i−i-1-111
χ1722222222222222222222-2-2-2222-2-2-2-2-22-2-2-2-200000000000000000000000022-2-222-2-2000000000000000000000000
χ1822222222222222222222-2-2-2222-2-2-2-2-22-2-2-2-2000000000000000000000000-2-222-2-222000000000000000000000000
χ192222222222222222-2-2-2-2222-2-2-222222-2-2-2-2-2000000000000000022-2-222-2-200000000000000000000000000000000
χ202222222222222222-2-2-2-2222-2-2-222222-2-2-2-2-20000000000000000-2-222-2-22200000000000000000000000000000000
χ212222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000000000002-22-20000
χ222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000-22-220000
χ2322222-2-22-2-22-2-2-2-2200002-2-200022-2-2200000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2002i−2i002i−2i0000000022−2−222−2−20000000000000000
χ2422222-2-22-2-22-2-2-2-2200002-2-200022-2-2200000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i200−2i2i00−2i2i00000000−2−222−2−2220000000000000000
χ2522222-2-22-2-22-2-2-2-2200002-2-200022-2-2200000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2002i−2i002i−2i00000000−2−222−2−2220000000000000000
χ2622222-2-22-2-22-2-2-2-2200002-2-200022-2-2200000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200−2i2i00−2i2i0000000022−2−222−2−20000000000000000
χ272222-22-2-22-2-2-22-22-222-2-20002-2-20000020000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000002-2002-200000000i2i2−i2−i2i2i2−i2−i200000000
χ282222-22-2-22-2-2-22-22-222-2-20002-2-20000020000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000-2200-2200000000−i2−i2i2i2−i2−i2i2i200000000
χ292222-22-2-22-2-2-22-22-222-2-20002-2-20000020000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000002-2002-200000000−i2−i2i2i2−i2−i2i2i200000000
χ302222-22-2-22-2-2-22-22-222-2-20002-2-20000020000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000-2200-2200000000i2i2−i2−i2i2i2−i2−i200000000
χ3122-2-22-22-22-2-2-2-222222-2-2000-22200000-2000022−2−222−2−2−2−222−2−22200000000002i−2i00−2i2i00000000−i2−i2i2i2i2i2−i2−i200000000
χ3222-2-22-22-22-2-2-2-222222-2-2000-22200000-2000022−2−222−2−2−2−222−2−2220000000000−2i2i002i−2i00000000i2i2−i2−i2−i2−i2i2i200000000
χ3322-2-22-22-22-2-2-2-222222-2-2000-22200000-20000−2−222−2−22222−2−222−2−200000000002i−2i00−2i2i00000000i2i2−i2−i2−i2−i2i2i200000000
χ3422-2-22-22-22-2-2-2-222222-2-2000-22200000-20000−2−222−2−22222−2−222−2−20000000000−2i2i002i−2i00000000−i2−i2i2i2i2i2−i2−i200000000
χ3522-2-2-2222-2-22-222-2-200002-2-2000-2-2222000002222−2−2−2−2−2−2−2−22222002i−2i00−2i2i00000000−i2−i2i2i2i2i2−i2−i20000000000000000
χ3622-2-2-2222-2-22-222-2-200002-2-2000-2-2222000002222−2−2−2−2−2−2−2−2222200−2i2i002i−2i00000000i2i2−i2−i2−i2−i2i2i20000000000000000
χ3722-2-2-2222-2-22-222-2-200002-2-2000-2-222200000−2−2−2−222222222−2−2−2−2002i−2i00−2i2i00000000i2i2−i2−i2−i2−i2i2i20000000000000000
χ3822-2-2-2222-2-22-222-2-200002-2-2000-2-222200000−2−2−2−222222222−2−2−2−200−2i2i002i−2i00000000−i2−i2i2i2i2i2−i2−i20000000000000000
χ3922-2-2-2-2-222222-2-22-22222-2-2-2-2-2-22222-2-2-2-2220000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ4022-2-2-2-2-222222-2-22-22222-2-2-2-2-2-22222-2-2-2-222000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ4122-2-2-2-2-222222-2-22-2-2-2-2-2222222-2-2-2-222-2-222000000000000000022-2-2-2-22200000000000000000000000000000000
χ4222-2-2-2-2-222222-2-22-2-2-2-2-2222222-2-2-2-222-2-2220000000000000000-2-22222-2-200000000000000000000000000000000
χ4322-2-2-2-2-222222-2-22-2-2-2-2-2-2-2-22222222-2222-2-20000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ4422-2-2-2-2-222222-2-22-2-2-2-2-2-2-2-22222222-2222-2-2000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ452-22-2222222-2-2-2-2-2-22-22-222-222-22-22-2-2-22-2-222-22-22-22-22-22-22-22-20000000000000000000000000000000000000000
χ462-22-2222222-2-2-2-2-2-22-22-222-222-22-22-2-2-22-2-22-22-22-22-22-22-22-22-220000000000000000000000000000000000000000
χ472-22-2222222-2-2-2-2-2-22-22-2-2-2222-2-22-222-2-222-200000000000000000000000000000000000000002-22-22-22-200000000
χ482-22-2222222-2-2-2-2-2-22-22-2-2-2222-2-22-222-2-222-20000000000000000000000000000000000000000-22-22-22-2200000000
χ492-22-2222222-2-2-2-2-2-2-22-2222-2-2-222-22-2-22-222-2000000000000000000000000000000002-22-22-22-20000000000000000
χ502-22-2222222-2-2-2-2-2-2-22-2222-2-2-222-22-2-22-222-200000000000000000000000000000000-22-22-22-220000000000000000
χ512-22-2222222-2-2-2-2-2-2-22-22-2-22-2-22-22-22222-2-2200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ522-22-2222222-2-2-2-2-2-2-22-22-2-22-2-22-22-22222-2-220000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ532-22-22-2-22-2-2-22222-200002-220002-2-22-200000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i22i−2i002i−2i00000000002−2−222−2−220000000000000000
χ542-22-22-2-22-2-2-22222-200002-220002-2-22-200000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2−2i2i00−2i2i0000000000−222−2−222−20000000000000000
χ552-22-22-2-22-2-2-22222-200002-220002-2-22-200000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i22i−2i002i−2i0000000000−222−2−222−20000000000000000
χ562-22-22-2-22-2-2-22222-200002-220002-2-22-200000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−2i2i00−2i2i00000000002−2−222−2−220000000000000000
χ572-22-2-22-2-22-222-22-222-2-220002-2200000-20000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000002-2002-20000000000i2−i2−i2i2i2−i2−i2i200000000
χ582-22-2-22-2-22-222-22-222-2-220002-2200000-20000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000-2200-220000000000−i2i2i2−i2−i2i2i2−i200000000
χ592-22-2-22-2-22-222-22-222-2-220002-2200000-20000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000002-2002-20000000000−i2i2i2−i2−i2i2i2−i200000000
χ602-22-2-22-2-22-222-22-222-2-220002-2200000-20000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000-2200-220000000000i2−i2−i2i2i2−i2−i2i200000000
χ612-2-222-22-22-2222-2-2-22-2-22000-22-200000200002−2−222−2−22−222−2−222−2000000002i−2i00−2i2i0000000000−i2i2i2−i2i2−i2−i2i200000000
χ622-2-222-22-22-2222-2-2-22-2-22000-22-200000200002−2−222−2−22−222−2−222−200000000−2i2i002i−2i0000000000i2−i2−i2i2−i2i2i2−i200000000
χ632-2-222-22-22-2222-2-2-22-2-22000-22-20000020000−222−2−222−22−2−222−2−22000000002i−2i00−2i2i0000000000i2−i2−i2i2−i2i2i2−i200000000
χ642-2-222-22-22-2222-2-2-22-2-22000-22-20000020000−222−2−222−22−2−222−2−2200000000−2i2i002i−2i0000000000−i2i2i2−i2i2−i2−i2i200000000
χ652-2-22-2222-2-2-22-2-22200002-22000-222-2-2000002−22−2−22−22−22−222−22−22i−2i00−2i2i0000000000−i2i2i2−i2i2−i2−i2i20000000000000000
χ662-2-22-2222-2-2-22-2-22200002-22000-222-2-2000002−22−2−22−22−22−222−22−2−2i2i002i−2i0000000000i2−i2−i2i2−i2i2i2−i20000000000000000
χ672-2-22-2222-2-2-22-2-22200002-22000-222-2-200000−22−222−22−22−22−2−22−222i−2i00−2i2i0000000000i2−i2−i2i2−i2i2i2−i20000000000000000
χ682-2-22-2222-2-2-22-2-22200002-22000-222-2-200000−22−222−22−22−22−2−22−22−2i2i002i−2i0000000000−i2i2i2−i2i2−i2−i2i20000000000000000
χ692-2-22-2-2-2222-2-222-222-22-222-2-2-22-22-22-222-22-22i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000
χ702-2-22-2-2-2222-2-222-222-22-222-2-2-22-22-22-222-22-2−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000
χ712-2-22-2-2-2222-2-222-222-22-2-2-22-2-222-22-222-22-2200000000000000000000000000000000000000002-22-2-22-2200000000
χ722-2-22-2-2-2222-2-222-222-22-2-2-22-2-222-22-222-22-220000000000000000000000000000000000000000-22-222-22-200000000
χ732-2-22-2-2-2222-2-222-22-22-2222-222-2-22-22-2-2-22-22000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ742-2-22-2-2-2222-2-222-22-22-2222-222-2-22-22-2-2-22-2200000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ752-2-22-2-2-2222-2-222-22-22-22-2-2222-22-22-22-22-22-200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ762-2-22-2-2-2222-2-222-22-22-22-2-2222-22-22-22-22-22-20000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ7744444-4-44-4-44-4-4-4-440000-444000-4-444-40000000000000000000000000000000000000000000000000000000000000
χ784444-44-4-44-4-4-44-44-4-4-444000-44400000-4000000000000000000000000000000000000000000000000000000000000
χ794444-4-44-4-44-44-44-4-40000000000000000000022-2-2-2-22222-2-2-2-2220000000000000000000000000000000000000000
χ804444-4-44-4-44-44-44-4-400000000000000000000-2-22222-2-2-2-22222-2-20000000000000000000000000000000000000000
χ8144-4-444-4-4-44-444-4-44000000000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ8244-4-444-4-4-44-444-4-4400000000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ8344-4-44-44-44-4-4-4-4444-4-4440004-4-4000004000000000000000000000000000000000000000000000000000000000000
χ8444-4-4-4444-4-44-444-4-40000-44400044-4-4-40000000000000000000000000000000000000000000000000000000000000
χ854-44-44-4-44-4-4-44444-40000-44-4000-444-440000000000000000000000000000000000000000000000000000000000000
χ864-44-4-44-4-44-444-44-44-444-4000-44-4000004000000000000000000000000000000000000000000000000000000000000
χ874-44-4-4-44-4-444-44-444000000000000000000002-2-22-222-22-2-22-222-20000000000000000000000000000000000000000
χ884-44-4-4-44-4-444-44-44400000000000000000000-222-22-2-22-222-22-2-220000000000000000000000000000000000000000
χ894-4-4444-4-4-444-4-444-4000000000000000000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000
χ904-4-4444-4-4-444-4-444-400000000000000000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000000000
χ914-4-444-44-44-4444-4-4-4-444-40004-4400000-4000000000000000000000000000000000000000000000000000000000000
χ924-4-44-4444-4-4-44-4-4440000-44-40004-4-4440000000000000000000000000000000000000000000000000000000000000

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