Finite Group Databasebeta

← Group #315607

Character table — Group #315607

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222222222222222222224444444444444444444444444444444444444444444444161616161616161632323232
order12222222222244444444444488888888888888884444448888888888888888888888888888888888888888444444442444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1
χ911111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ1111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ1211111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ1311111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1111-1-11
χ1411111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1-111-1
χ1511111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-111-1
χ1611111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-11-1-11
χ1722222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000000000002222-2-2-2-2000000000000
χ1822222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000000000000000-2-2-2-22222000000000000
χ19222222222222-2-22222-2-2-2-2-2-20000000000000000-2-222-2-200000000000000002222-2-2-2-22222-2-2-2-200000000000000000000
χ20222222222222-2-22222-2-2-2-2-2-20000000000000000-2-222-2-20000000000000000-2-2-2-22222-2-2-2-2222200000000000000000000
χ21222222222222-2-2-2-2-2-22222-2-20000000000000000-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ22222222222222-2-2-2-2-2-22222-2-20000000000000000-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ2322222222-2-2-2-222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000-2-2-2-22222000000000000
χ2422222222-2-2-2-222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222-2-22222000000000000000000000000000000002222-2-2-2-2000000000000
χ2522222222-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000022-2-22200000000000000002222-2-2-2-2-2-2-2-2222200000000000000000000
χ2622222222-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000022-2-2220000000000000000-2-2-2-222222222-2-2-2-200000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-200000000000000002222-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-200000000000000002222-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000
χ2922-22-2-22-222-2-20022-2-2000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2002-20022−2−222−2−222−2−222−2−200002i2i−2i−2i00002i2i−2i−2ii2i2−i2−i2i2i2−i2−i2000000000000
χ3022-22-2-22-222-2-20022-2-2000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2002-200−2−222−2−222−2−222−2−2220000−2i−2i2i2i0000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2000000000000
χ3122-22-2-22-222-2-20022-2-2000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2002-20022−2−222−2−222−2−222−2−20000−2i−2i2i2i0000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i2000000000000
χ3222-22-2-22-222-2-20022-2-2000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2002-200−2−222−2−222−2−222−2−22200002i2i−2i−2i00002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2000000000000
χ3322-22-2-22-222-2-200-2-222000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i200-220022−2−2−2−22222−2−2−2−2222i2i−2i−2i00002i2i−2i−2i0000i2i2−i2−i2−i2−i2i2i2000000000000
χ3422-22-2-22-222-2-200-2-222000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i200-2200−2−22222−2−2−2−22222−2−2−2i−2i2i2i0000−2i−2i2i2i0000i2i2−i2−i2−i2−i2i2i2000000000000
χ3522-22-2-22-222-2-200-2-222000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i200-220022−2−2−2−22222−2−2−2−222−2i−2i2i2i0000−2i−2i2i2i0000−i2−i2i2i2i2i2−i2−i2000000000000
χ3622-22-2-22-222-2-200-2-222000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i200-2200−2−22222−2−2−2−22222−2−22i2i−2i−2i00002i2i−2i−2i0000−i2−i2i2i2i2i2−i2−i2000000000000
χ3722-22-2-22-2-2-2220022-2-2000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i200-220022−2−222−2−2−2−222−2−22200002i2i−2i−2i0000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i2000000000000
χ3822-22-2-22-2-2-2220022-2-2000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i200-2200−2−222−2−22222−2−222−2−20000−2i−2i2i2i00002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2000000000000
χ3922-22-2-22-2-2-2220022-2-2000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200-220022−2−222−2−2−2−222−2−2220000−2i−2i2i2i00002i2i−2i−2ii2i2−i2−i2i2i2−i2−i2000000000000
χ4022-22-2-22-2-2-2220022-2-2000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200-2200−2−222−2−22222−2−222−2−200002i2i−2i−2i0000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2000000000000
χ4122-22-2-22-2-2-22200-2-222000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2002-20022−2−2−2−222−2−22222−2−22i2i−2i−2i0000−2i−2i2i2i0000−i2−i2i2i2i2i2−i2−i2000000000000
χ4222-22-2-22-2-2-22200-2-222000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2002-200−2−22222−2−222−2−2−2−222−2i−2i2i2i00002i2i−2i−2i0000−i2−i2i2i2i2i2−i2−i2000000000000
χ4322-22-2-22-2-2-22200-2-222000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2002-20022−2−2−2−222−2−22222−2−2−2i−2i2i2i00002i2i−2i−2i0000i2i2−i2−i2−i2−i2i2i2000000000000
χ4422-22-2-22-2-2-22200-2-222000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2002-200−2−22222−2−222−2−2−2−2222i2i−2i−2i0000−2i−2i2i2i0000i2i2−i2−i2−i2−i2i2i2000000000000
χ452-22-22-22-22-22-22-2000000002-2000000002i2i−2i−2i2i2i−2i−2i2-200002−22−22−22−22−22−22−22−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200002i−2i2i−2i000000000000
χ462-22-22-22-22-22-22-2000000002-2000000002i2i−2i−2i2i2i−2i−2i2-20000−22−22−22−22−22−22−22−22−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200002i−2i2i−2i000000000000
χ472-22-22-22-22-22-22-2000000002-200000000−2i−2i2i2i−2i−2i2i2i2-200002−22−22−22−22−22−22−22−2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000−2i2i−2i2i000000000000
χ482-22-22-22-22-22-22-2000000002-200000000−2i−2i2i2i−2i−2i2i2i2-20000−22−22−22−22−22−22−22−22i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000−2i2i−2i2i000000000000
χ492-22-22-22-22-22-2-2200000000-222i2i−2i−2i2i2i−2i−2i00000000-2200002−22−2−22−222−22−2−22−22i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i22i−2i2i−2i0000000000000000
χ502-22-22-22-22-22-2-2200000000-222i2i−2i−2i2i2i−2i−2i00000000-220000−22−222−22−2−22−222−22−2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i22i−2i2i−2i0000000000000000
χ512-22-22-22-22-22-2-2200000000-22−2i−2i2i2i−2i−2i2i2i00000000-2200002−22−2−22−222−22−2−22−22−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−2i2i−2i2i0000000000000000
χ522-22-22-22-22-22-2-2200000000-22−2i−2i2i2i−2i−2i2i2i00000000-220000−22−222−22−2−22−222−22−2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2−2i2i−2i2i0000000000000000
χ532-22-22-22-2-22-222-2000000002-2000000002i2i−2i−2i2i2i−2i−2i-2200002−22−22−22−2−22−22−22−22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000−2i2i−2i2i000000000000
χ542-22-22-22-2-22-222-2000000002-2000000002i2i−2i−2i2i2i−2i−2i-220000−22−22−22−222−22−22−22−2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000−2i2i−2i2i000000000000
χ552-22-22-22-2-22-222-2000000002-200000000−2i−2i2i2i−2i−2i2i2i-2200002−22−22−22−2−22−22−22−22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200002i−2i2i−2i000000000000
χ562-22-22-22-2-22-222-2000000002-200000000−2i−2i2i2i−2i−2i2i2i-220000−22−22−22−222−22−22−22−2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200002i−2i2i−2i000000000000
χ572-22-22-22-2-22-22-2200000000-222i2i−2i−2i2i2i−2i−2i000000002-200002−22−2−22−22−22−222−22−2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2−2i2i−2i2i0000000000000000
χ582-22-22-22-2-22-22-2200000000-222i2i−2i−2i2i2i−2i−2i000000002-20000−22−222−22−22−22−2−22−22−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−2i2i−2i2i0000000000000000
χ592-22-22-22-2-22-22-2200000000-22−2i−2i2i2i−2i−2i2i2i000000002-200002−22−2−22−22−22−222−22−2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i22i−2i2i−2i0000000000000000
χ602-22-22-22-2-22-22-2200000000-22−2i−2i2i2i−2i−2i2i2i000000002-20000−22−222−22−22−22−2−22−22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i22i−2i2i−2i0000000000000000
χ612-2-2222-2-20000-2-22-22-222-2-2222-22-22-22-22-22-22-22-20000000000000000000000000000000000000000000000002i−2i002i−2i0000
χ622-2-2222-2-20000-2-22-22-222-2-2222-22-22-22-22-22-22-22-2000000000000000000000000000000000000000000000000−2i2i00−2i2i0000
χ632-2-2222-2-20000-2-22-22-222-2-222-22-22-22-22-22-22-22-220000000000000000000000000000000000000000000000002i−2i00−2i2i0000
χ642-2-2222-2-20000-2-22-22-222-2-222-22-22-22-22-22-22-22-22000000000000000000000000000000000000000000000000−2i2i002i−2i0000
χ652-2-2222-2-20000-2-2-22-22-2-222222-22-22-22-2-22-22-22-2200000000000000000000000000000000000000000000002i−2i002i−2i000000
χ662-2-2222-2-20000-2-2-22-22-2-222222-22-22-22-2-22-22-22-220000000000000000000000000000000000000000000000−2i2i00−2i2i000000
χ672-2-2222-2-20000-2-2-22-22-2-22222-22-22-22-222-22-22-22-200000000000000000000000000000000000000000000002i−2i00−2i2i000000
χ682-2-2222-2-20000-2-2-22-22-2-22222-22-22-22-222-22-22-22-20000000000000000000000000000000000000000000000−2i2i002i−2i000000
χ692-2-2-2-22222-2-220000002-22-20022−2−2−2−22222−2−2−2−22200002-200002-2-2200002-2-222−2−222−2−222−2−222−2−222−2−222−2−22000000000000
χ702-2-2-2-22222-2-220000002-22-20022−2−2−2−22222−2−2−2−22200002-20000-222-20000-222-2−222−2−222−2−222−2−222−22−2−222−2−22000000000000
χ712-2-2-2-22222-2-220000002-22-200−2−22222−2−2−2−22222−2−200002-200002-2-2200002-2-22−222−2−222−2−222−2−222−2−222−2−222−2000000000000
χ722-2-2-2-22222-2-220000002-22-200−2−22222−2−2−2−22222−2−200002-20000-222-20000-222-22−2−222−2−222−2−222−2−22−222−2−222−2000000000000
χ732-2-2-2-22222-2-22000000-22-220022−2−2−2−222−2−22222−2−20000-222-2-2200002-2-2200002−2−22−222−22−2−22−222−22−2−22−222−2000000000000
χ742-2-2-2-22222-2-22000000-22-220022−2−2−2−222−2−22222−2−20000-22-222-20000-222-20000−222−22−2−22−222−22−2−222−2−22−222−2000000000000
χ752-2-2-2-22222-2-22000000-22-2200−2−22222−2−222−2−2−2−2220000-222-2-2200002-2-220000−222−22−2−22−222−22−2−22−222−22−2−22000000000000
χ762-2-2-2-22222-2-22000000-22-2200−2−22222−2−222−2−2−2−2220000-22-222-20000-222-200002−2−22−222−22−2−22−222−2−222−22−2−22000000000000
χ772-2-2-2-2222-222-20000002-22-20022−2−2−2−22222−2−2−2−2220000-2200002-2-220000-222-22−2−222−2−22−222−2−222−2−222−2−222−2000000000000
χ782-2-2-2-2222-222-20000002-22-20022−2−2−2−22222−2−2−2−2220000-220000-222-200002-2-22−222−2−222−22−2−222−2−22−222−2−222−2000000000000
χ792-2-2-2-2222-222-20000002-22-200−2−22222−2−2−2−22222−2−20000-2200002-2-220000-222-2−222−2−222−22−2−222−2−222−2−222−2−22000000000000
χ802-2-2-2-2222-222-20000002-22-200−2−22222−2−2−2−22222−2−20000-220000-222-200002-2-222−2−222−2−22−222−2−222−22−2−222−2−22000000000000
χ812-2-2-2-2222-222-2000000-22-220022−2−2−2−222−2−22222−2−200002-22-2-220000-222-200002−2−22−222−2−222−22−2−22−222−22−2−22000000000000
χ822-2-2-2-2222-222-2000000-22-220022−2−2−2−222−2−22222−2−200002-2-222-200002-2-220000−222−22−2−222−2−22−222−2−222−22−2−22000000000000
χ832-2-2-2-2222-222-2000000-22-2200−2−22222−2−222−2−2−2−22200002-22-2-220000-222-20000−222−22−2−222−2−22−222−22−2−22−222−2000000000000
χ842-2-2-2-2222-222-2000000-22-2200−2−22222−2−222−2−2−2−22200002-2-222-200002-2-2200002−2−22−222−2−222−22−2−222−2−22−222−2000000000000
χ85444-4-44-4-400000000004-4-440022−22−2222−222222−2222−22−2222−222222−220000000000000000000000000000000000000000000000000000000000
χ86444-4-44-4-400000000004-4-4400−222222−2222−22−2222−222222−2222−22−22220000000000000000000000000000000000000000000000000000000000
χ87444-4-44-4-40000000000-444-40022−22−2222−222222−22−222222−2222−22−22220000000000000000000000000000000000000000000000000000000000
χ88444-4-44-4-40000000000-444-400−222222−2222−22−222222−22−2222−222222−220000000000000000000000000000000000000000000000000000000000
χ8944-4-44-4-4400004-400000000-444i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000
χ9044-4-44-4-4400004-400000000-44−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000
χ9144-4-44-4-440000-44000000004-4000000004i−4i−4i4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ9244-4-44-4-440000-44000000004-400000000−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ934-444-4-4-440000004-4-440000002i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000000000000000000000
χ944-444-4-4-440000004-4-44000000−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000000000000000000000
χ954-444-4-4-44000000-444-40000002i2−2i22i2−2i2−2i22i2−2i22i2−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000000000000000000000
χ964-444-4-4-44000000-444-4000000−2i22i2−2i22i22i2−2i22i2−2i22i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000000000000000000000
χ974-4-4444-4-40000444-44-4-4-444-4-400000000000000000000000000000000000000000000000000000000000000000000000000
χ984-4-4444-4-4000044-44-4444-4-4-4-400000000000000000000000000000000000000000000000000000000000000000000000000

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