Finite Group Databasebeta

← Group #495039

Character table — Group #495039

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111122222222222222222244444444444444444444444444444444444444444444444444444416161616161616161616161616161616
order1222222222444444448888444444448888888888888816161616161616161616161616161616161616161616161616161616161616164444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ9111111-1-1-1-11-1-1-1-1111111111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111-1-1-1-11-1-1-1-1111111111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111-1-1-1-11-1-1-1-1111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ12111111-1-1-1-11-1-1-1-1111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ13111111-1-1-1-11-1-1-1-11111111-1-111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ14111111-1-1-1-11-1-1-1-11111111-1-111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ15111111-1-1-1-11-1-1-1-11111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1
χ16111111-1-1-1-11-1-1-1-11111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ1711-1-11-111-1-1-111-1-11-1111-1-1i−ii−ii−ii−i1-111-1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−ii−ii−i1-11-11-11-1
χ1811-1-11-111-1-1-111-1-11-1111-1-1i−ii−ii−ii−i1-111-1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii−ii−ii-11-11-11-11
χ1911-1-11-111-1-1-111-1-11-1111-1-1i−ii−ii−ii−i1-111-1-1ii−i−iii−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiii−ii−i−ii−ii1-11-1-11-11
χ2011-1-11-111-1-1-111-1-11-1111-1-1i−ii−ii−ii−i1-111-1-1ii−i−iii−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii−ii−iii−ii−i-11-111-11-1
χ2111-1-11-111-1-1-111-1-11-1111-1-1−ii−ii−ii−ii1-111-1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−ii−ii−i-11-11-11-11
χ2211-1-11-111-1-1-111-1-11-1111-1-1−ii−ii−ii−ii1-111-1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−ii−ii1-11-11-11-1
χ2311-1-11-111-1-1-111-1-11-1111-1-1−ii−ii−ii−ii1-111-1-1−i−iii−i−iii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−ii−ii−i−ii−ii-11-111-11-1
χ2411-1-11-111-1-1-111-1-11-1111-1-1−ii−ii−ii−ii1-111-1-1−i−iii−i−iii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−ii−iii−ii−i1-11-1-11-11
χ2511-1-11-1-1-111-1-1-1111-1111-1-1i−i−iii−i−ii1-1-1-111ii−i−i−i−iii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiii−i−iii−i−ii1-1-111-1-11
χ2611-1-11-1-1-111-1-1-1111-1111-1-1i−i−iii−i−ii1-1-1-111ii−i−i−i−iii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−iii−i−iii−i-111-1-111-1
χ2711-1-11-1-1-111-1-1-1111-1111-1-1i−i−iii−i−ii1-1-1-111ii−i−i−i−iii-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−ii−i−ii−iii−i1-1-11-111-1
χ2811-1-11-1-1-111-1-1-1111-1111-1-1i−i−iii−i−ii1-1-1-111ii−i−i−i−iii-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−iii−ii−i−ii-111-11-1-11
χ2911-1-11-1-1-111-1-1-1111-1111-1-1−iii−i−iii−i1-1-1-111−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−ii−i−iii−i−ii-111-1-111-1
χ3011-1-11-1-1-111-1-1-1111-1111-1-1−iii−i−iii−i1-1-1-111−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−iii−i1-1-111-1-11
χ3111-1-11-1-1-111-1-1-1111-1111-1-1−iii−i−iii−i1-1-1-111−i−iiiii−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiii−i−ii−iii−i-111-11-1-11
χ3211-1-11-1-1-111-1-1-1111-1111-1-1−iii−i−iii−i1-1-1-111−i−iiiii−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−iii−ii−i−ii1-1-11-111-1
χ33222222222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ34222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000000000000000
χ352222222222-2-2-2-2-2-2-2-20000000000000000002i−2i2i−2i2i−2i2i−2i22−2−222−2−222−2−222−2−2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ362222222222-2-2-2-2-2-2-2-20000000000000000002i−2i2i−2i2i−2i2i−2i−2−222−2−222−2−222−2−222−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ372222222222-2-2-2-2-2-2-2-2000000000000000000−2i2i−2i2i−2i2i−2i2i22−2−222−2−222−2−222−2−2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ382222222222-2-2-2-2-2-2-2-2000000000000000000−2i2i−2i2i−2i2i−2i2i−2−222−2−222−2−222−2−222i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ39222222-2-2-2-22-2-2-2-2222-2-2-2-222-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000
χ40222222-2-2-2-22-2-2-2-2222-2-2-2-2-2-222-2-222-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000
χ41222222-2-2-2-2-22222-2-2-20000000000000000002i−2i2i−2i−2i2i−2i2i22−2−222−2−2−2−222−2−222i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ42222222-2-2-2-2-22222-2-2-20000000000000000002i−2i2i−2i−2i2i−2i2i−2−222−2−22222−2−222−2−2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ43222222-2-2-2-2-22222-2-2-2000000000000000000−2i2i−2i2i2i−2i2i−2i22−2−222−2−2−2−222−2−222−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ44222222-2-2-2-2-22222-2-2-2000000000000000000−2i2i−2i2i2i−2i2i−2i−2−222−2−22222−2−222−2−2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ452222-2-22-22-222-22-2-2-2200002222-2-2-2-2000000000000002−22−22−22−22−22−22−22−22−22−22−22−22−22−22−22−20000000000000000
χ462222-2-22-22-222-22-2-2-2200002222-2-2-2-200000000000000−22−22−22−22−22−22−22−22−22−22−22−22−22−22−22−220000000000000000
χ472222-2-22-22-222-22-2-2-220000-2-2-2-22222000000000000002−22−22−22−22−22−22−22−2−22−22−22−22−22−22−22−220000000000000000
χ482222-2-22-22-222-22-2-2-220000-2-2-2-2222200000000000000−22−22−22−22−22−22−22−222−22−22−22−22−22−22−22−20000000000000000
χ492222-2-22-22-2-2-22-2222-2222200000000-2-22-22-2000000002-2-222-2-222-2-222-2-2200000000000000000000000000000000
χ502222-2-22-22-2-2-22-2222-2222200000000-2-22-22-200000000-222-2-222-2-222-2-222-200000000000000000000000000000000
χ512222-2-22-22-2-2-22-2222-2-2-2-2-20000000022-22-220000000000000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i0000000000000000
χ522222-2-22-22-2-2-22-2222-2-2-2-2-20000000022-22-22000000000000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i0000000000000000
χ532222-2-2-22-222-22-22-2-22000022-2-2-2-222000000000000002−22−22−22−2−22−22−22−222−22−22−22−2−22−22−22−220000000000000000
χ542222-2-2-22-222-22-22-2-22000022-2-2-2-22200000000000000−22−22−22−222−22−22−22−2−22−22−22−222−22−22−22−20000000000000000
χ552222-2-2-22-222-22-22-2-220000-2-22222-2-2000000000000002−22−22−22−2−22−22−22−22−22−22−22−222−22−22−22−20000000000000000
χ562222-2-2-22-222-22-22-2-220000-2-22222-2-200000000000000−22−22−22−222−22−22−22−22−22−22−22−2−22−22−22−220000000000000000
χ572222-2-2-22-22-22-22-222-2222200000000-2-2-22-22000000002-2-222-2-22-222-2-222-200000000000000000000000000000000
χ582222-2-2-22-22-22-22-222-2222200000000-2-2-22-2200000000-222-2-222-22-2-222-2-2200000000000000000000000000000000
χ592222-2-2-22-22-22-22-222-2-2-2-2-200000000222-22-20000000000000000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i0000000000000000
χ602222-2-2-22-22-22-22-222-2-2-2-2-200000000222-22-2000000000000000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i0000000000000000
χ6122-2-22-222-2-22-2-222-22-20000000000000000002-2-222-2-2222−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−2220000000000000000
χ6222-2-22-222-2-22-2-222-22-20000000000000000002-2-222-2-22−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−22222−2−20000000000000000
χ6322-2-22-222-2-22-2-222-22-2000000000000000000-222-2-222-222−2−2−2−22222−2−2−2−222−2−22222−2−2−2−22222−2−20000000000000000
χ6422-2-22-222-2-22-2-222-22-2000000000000000000-222-2-222-2−2−22222−2−2−2−22222−2−222−2−2−2−22222−2−2−2−2220000000000000000
χ6522-2-22-222-2-2-222-2-22-22-2-2222i−2i2i−2i2i−2i2i−2i-22-2-222−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ6622-2-22-222-2-2-222-2-22-22-2-222−2i2i−2i2i−2i2i−2i2i-22-2-2222i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ6722-2-22-2-2-222222-2-2-22-20000000000000000002-2-22-222-222−2−2−2−222−2−22222−2−222−2−2−2−222−2−22222−2−20000000000000000
χ6822-2-22-2-2-222222-2-2-22-20000000000000000002-2-22-222-2−2−22222−2−222−2−2−2−222−2−22222−2−222−2−2−2−2220000000000000000
χ6922-2-22-2-2-222222-2-2-22-2000000000000000000-222-22-2-2222−2−2−2−222−2−22222−2−2−2−22222−2−222−2−2−2−2220000000000000000
χ7022-2-22-2-2-222222-2-2-22-2000000000000000000-222-22-2-22−2−22222−2−222−2−2−2−22222−2−2−2−222−2−22222−2−20000000000000000
χ7122-2-22-2-2-222-2-2-2222-22-2-2222i−2i−2i2i2i−2i−2i2i-2222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ7222-2-22-2-2-222-2-2-2222-22-2-222−2i2i2i−2i−2i2i2i−2i-2222-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ7322-2-2-222-2-222-222-22-2-222-2-200000000-222-2-22000000002-2-22-222-22-2-22-222-200000000000000000000000000000000
χ7422-2-2-222-2-222-222-22-2-222-2-200000000-222-2-2200000000-222-22-2-22-222-22-2-2200000000000000000000000000000000
χ7522-2-2-222-2-222-222-22-2-2-2-222000000002-2-222-20000000000000000000000002-2-22-222-22-2-22-222-20000000000000000
χ7622-2-2-222-2-222-222-22-2-2-2-222000000002-2-222-2000000000000000000000000-222-22-2-22-222-22-2-220000000000000000
χ7722-2-2-222-2-22-22-2-22-22200002i−2i2i−2i−2i2i−2i2i000000000000002−22−2−22−222−22−2−22−22i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ7822-2-2-222-2-22-22-2-22-22200002i−2i2i−2i−2i2i−2i2i00000000000000−22−222−22−2−22−222−22−2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ7922-2-2-222-2-22-22-2-22-2220000−2i2i−2i2i2i−2i2i−2i000000000000002−22−2−22−222−22−2−22−22−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ8022-2-2-222-2-22-22-2-22-2220000−2i2i−2i2i2i−2i2i−2i00000000000000−22−222−22−2−22−222−22−2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ8122-2-2-22-222-222-2-222-2-222-2-200000000-22-222-2000000002-2-22-222-2-222-22-2-2200000000000000000000000000000000
χ8222-2-2-22-222-222-2-222-2-222-2-200000000-22-222-200000000-222-22-2-222-2-22-222-200000000000000000000000000000000
χ8322-2-2-22-222-222-2-222-2-2-2-222000000002-22-2-220000000000000000000000002-2-22-222-2-222-22-2-220000000000000000
χ8422-2-2-22-222-222-2-222-2-2-2-222000000002-22-2-22000000000000000000000000-222-22-2-222-2-22-222-20000000000000000
χ8522-2-2-22-222-2-2-222-2-22200002i−2i−2i2i−2i2i2i−2i000000000000002−22−2−22−22−22−222−22−2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ8622-2-2-22-222-2-2-222-2-22200002i−2i−2i2i−2i2i2i−2i00000000000000−22−222−22−22−22−2−22−22−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ8722-2-2-22-222-2-2-222-2-2220000−2i2i2i−2i2i−2i−2i2i000000000000002−22−2−22−22−22−222−22−2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ8822-2-2-22-222-2-2-222-2-2220000−2i2i2i−2i2i−2i−2i2i00000000000000−22−222−22−22−22−2−22−22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ898-88-80000000000000042−4242−420000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-800000000000000−4242−42420000000000000000000000000000000000000000000000000000000000000000000000
χ918-8-880000000000000042−42−42420000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-8800000000000000−424242−420000000000000000000000000000000000000000000000000000000000000000000000

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