Finite Group Databasebeta

← Group #203513

Character table — Group #203513

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128
size11111111111111111111111111111111222222222222222244444444444444444444444444444444444444444444444488888888888888888888888888888888
order12222222444444444444444444444444222244444444444488888888888888888888888888888888888888888888888844444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ7111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ101111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii
χ111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ121111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii
χ1711111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1811111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111-1-111-1-111−i−iii−i−iii−i−iii−i−iii
χ1911111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ2011111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-111-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i
χ2111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ2211111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111-1-111-1-111ii−i−iii−i−iii−i−iii−i−i
χ2311111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ2411111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-111-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-1
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1
χ3322222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-222-2-20000000000000000000000000000000000000000000000000000000000000000
χ3422222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222-2-2222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222-2-222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-22222-2-2-2-2-2-222-2-2-2-222-2-22222-2-20000000000000000000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-22222-2-2-2-2-2-2-2-22222-2-222-2-2-2-2220000000000000000000000000000000000000000000000000000000000000000
χ412222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-222-2-22222-2-2-2-2-2-2220000000000000000000000000000000022-2-222-2-222-2-222-2-200000000000000000000000000000000
χ422222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-222-2-22222-2-2-2-2-2-22200000000000000000000000000000000-2-222-2-222-2-222-2-22200000000000000000000000000000000
χ432222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-222-2-2-2-2222222-2-2000000000000000022-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ442222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-222-2-2-2-2222222-2-20000000000000000-2-222-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ452222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2222222-2-222-2-22222-2-2-2-2000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ462222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2222222-2-222-2-22222-2-2-2-200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ472222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-222-2-222-2-2-2-22222000000000000000022-2-222-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ482222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-222-2-222-2-2-2-222220000000000000000-2-222-2-22222-2-222-2-2000000000000000000000000000000000000000000000000
χ492222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-222-2-22222000000000000000022-2-2-2-22222-2-2-2-222000000000000000000000000000000000000000000000000
χ502222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-222-2-222220000000000000000-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000000000000000
χ512222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2222222-2-222-2-2-2-2000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ522222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2222222-2-222-2-2-2-200000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ532222-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-222-2-2-2-222-2-22222-2-2000000000000000022-2-2-2-222-2-22222-2-2000000000000000000000000000000000000000000000000
χ542222-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-222-2-2-2-222-2-22222-2-20000000000000000-2-22222-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ552222-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-22222-2-222-2-2-2-2220000000000000000000000000000000022-2-2-2-222-2-22222-2-200000000000000000000000000000000
χ562222-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-22222-2-222-2-2-2-22200000000000000000000000000000000-2-22222-2-222-2-2-2-22200000000000000000000000000000000
χ5722-2-222-2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2-22-22-22i−2i2i−2i2i−2i2-22i−2i0000000000000000000000000000000000000000000000000000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ
χ5822-2-222-2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2-22-22-22i−2i2i−2i2i−2i2-22i−2i000000000000000000000000000000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ
χ5922-2-222-2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i-22-22-22−2i2i−2i2i−2i2i-22−2i2i000000000000000000000000000000000000000000000000000000002i−2i2i−2i2-22-20000000000000000
χ6022-2-222-2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i-22-22-22−2i2i−2i2i−2i2i-22−2i2i00000000000000000000000000000000000000000000000000000000−2i2i−2i2i-22-220000000000000000
χ6122-2-222-2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i2-22-22-2−2i2i−2i2i−2i2i2-2−2i2i0000000000000000000000000000000000000000000000000000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3
χ6222-2-222-2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i2-22-22-2−2i2i−2i2i−2i2i2-2−2i2i000000000000000000000000000000000000000000000000000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3
χ6322-2-222-2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i-22-22-222i−2i2i−2i2i−2i-222i−2i000000000000000000000000000000000000000000000000000000002i−2i2i−2i-22-220000000000000000
χ6422-2-222-2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i-22-22-222i−2i2i−2i2i−2i-222i−2i00000000000000000000000000000000000000000000000000000000−2i2i−2i2i2-22-20000000000000000
χ6522-2-222-2-2-2-222-2-2222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2-22-2-22−2i2i−2i2i2i−2i-222i−2i000000000000000000000000000000000000000000000000000000002i−2i−2i2i2-2-220000000000000000
χ6622-2-222-2-2-2-222-2-2222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2-22-2-22−2i2i−2i2i2i−2i-222i−2i00000000000000000000000000000000000000000000000000000000−2i2i2i−2i-222-20000000000000000
χ6722-2-222-2-2-2-222-2-2222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i-22-222-22i−2i2i−2i−2i2i2-2−2i2i0000000000000000000000000000000000000000000000000000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3
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χ1254-4-44-444-44i−4i−4i4i−4i4i4i−4i4i−4i−4i4i−4i4i4i−4i-444-44-4-44000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1264-4-44-444-44i−4i−4i4i−4i4i4i−4i−4i4i4i−4i4i−4i−4i4i4-4-44-444-4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1274-4-44-444-4−4i4i4i−4i4i−4i−4i4i4i−4i−4i4i−4i4i4i−4i4-4-44-444-4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1284-4-44-444-4−4i4i4i−4i4i−4i−4i4i−4i4i4i−4i4i−4i−4i4i-444-44-4-44000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.