Finite Group Databasebeta

← Group #110842

Character table — Group #110842

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111111111111222222222222222222222222222222224444444444444444444444444444444444444444444488888888888888881616161616161616
order12222222444444442222444444444444888888888888888844444444444444444444888888888888888888888888444444448888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ911111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-111-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-111-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-11111111111-1-1iiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i1111-1-1-1-1-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-11111111111-1-1iiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-11111-1-111ii−i−i
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-11111111111-1-1−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i-1-1-1-1111111-1-1−i−iii
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-11111111111-1-1−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i
χ1711-1-1-1-1111111-1-1-1-11-1-1111-111-1-111-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-111-1-111-1-1ii−i−iii−i−i1-11-1i−ii−i
χ1811-1-1-1-1111111-1-1-1-11-1-1111-111-1-111-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1-1-111-1-111−i−iii−i−iii-11-11−ii−ii
χ1911-1-1-1-1111111-1-1-1-11-1-1111-111-1-111-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1-11-1ii−i−iii−i−i-1-1-1-11111-1-1-1-1111111-1-111-1-1ii−i−iii−i−i-11-11−ii−ii
χ2011-1-1-1-1111111-1-1-1-11-1-1111-111-1-111-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1-11-1ii−i−iii−i−i-1-1-1-11111-1-1-1-11111-1-111-1-111−i−iii−i−iii1-11-1i−ii−i
χ2111-1-1-1-1111111-1-1-1-11-1-1111-111-1-111-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1-11-1−i−iii−i−iii-1-1-1-11111-1-1-1-1111111-1-111-1-1−i−iii−i−iii-11-11i−ii−i
χ2211-1-1-1-1111111-1-1-1-11-1-1111-111-1-111-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1-11-1−i−iii−i−iii-1-1-1-11111-1-1-1-11111-1-111-1-111ii−i−iii−i−i1-11-1−ii−ii
χ2311-1-1-1-1111111-1-1-1-11-1-1111-111-1-111-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-111-1-111-1-1−i−iii−i−iii1-11-1−ii−ii
χ2411-1-1-1-1111111-1-1-1-11-1-1111-111-1-111-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1-1-111-1-111ii−i−iii−i−i-11-11i−ii−i
χ2511-1-1-1-111-1-1-1-11111-111-111-111-1-1-1-111-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii−i−iiiii−i−i-111-1-111-1
χ2611-1-1-1-111-1-1-1-11111-111-111-111-1-1-1-111-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−iii−i−i−i−iii1-1-111-1-11
χ2711-1-1-1-111-1-1-1-11111-111-111-111-1-1-1-111-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii−i−iiiii−i−i1-1-111-1-11
χ2811-1-1-1-111-1-1-1-11111-111-111-111-1-1-1-111-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−iii−i−i−i−iii-111-1-111-1
χ2911-1-1-1-111-1-1-1-11111-111-111-111-1-1-1-111-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-11-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iiiii−i−i−i−iii1-1-11-111-1
χ3011-1-1-1-111-1-1-1-11111-111-111-111-1-1-1-111-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-11-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i−i−iiiii−i−i-111-11-1-11
χ3111-1-1-1-111-1-1-1-11111-111-111-111-1-1-1-111-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iiiii−i−i−i−iii-111-11-1-11
χ3211-1-1-1-111-1-1-1-11111-111-111-111-1-1-1-111-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i−i−iiiii−i−i1-1-11-111-1
χ3322222222222222222222222-2-2-2-2-2-2-2-22000000000000000022-2-222-2-222-2-222-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ3422222222222222222222222-2-2-2-2-2-2-2-220000000000000000-2-222-2-222-2-222-2-222-2-2-2-2000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-222222222-222222222222222220000000000000000-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-2222222220000000000000000000000000000000000000000
χ372222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000002222000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ382222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000222200000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-22222-2-2-22222-2-2-2-2-22i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i0000000000000000-2-222−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-2-2-22222-2-2-2-2-2−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i0000000000000000-2-2222i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-22222-20000000000000000000000000000000022-2-20000000022-2-222-2-2-2-222-2-222000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-22222-20000000000000000000000000000000022-2-200000000-2-222-2-22222-2-222-2-2000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-2-2-222222000000000000000022-2-222-2-2-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-2-2-2222220000000000000000-2-222-2-22222-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ452222-2-2-2-222-2-222-2-222-2-22-2200000000-222−2−222−2−222−2−222−2−2002-2002-2002-2002-200002−22−22−22−22−22−22−22−22−22−22−22−2000000000000000000000000
χ462222-2-2-2-222-2-222-2-222-2-22-2200000000-222−2−222−2−222−2−222−2−200-2200-2200-2200-2200002−22−22−22−2−22−22−22−22−22−22−22−22000000000000000000000000
χ472222-2-2-2-222-2-222-2-222-2-22-2200000000-2−2−222−2−222−2−222−2−222002-2002-2002-2002-20000−22−22−22−22−22−22−22−22−22−22−22−22000000000000000000000000
χ482222-2-2-2-222-2-222-2-222-2-22-2200000000-2−2−222−2−222−2−222−2−22200-2200-2200-2200-220000−22−22−22−222−22−22−22−22−22−22−22−2000000000000000000000000
χ492222-2-2-2-222-2-222-2-2-2-222-22-200000000222−2−222−2−222−2−222−2−22i−2i002i−2i002i−2i002i−2i000000−22−22−22−22i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000000000000000
χ502222-2-2-2-222-2-222-2-2-2-222-22-200000000222−2−222−2−222−2−222−2−2−2i2i00−2i2i00−2i2i00−2i2i000000−22−22−22−22−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000000000000000
χ512222-2-2-2-222-2-222-2-2-2-222-22-2000000002−2−222−2−222−2−222−2−2222i−2i002i−2i002i−2i002i−2i0000002−22−22−22−2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000000000000000
χ522222-2-2-2-222-2-222-2-2-2-222-22-2000000002−2−222−2−222−2−222−2−222−2i2i00−2i2i00−2i2i00−2i2i0000002−22−22−22−2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000000000000000
χ532222-2-2-2-2-2-222-2-22222-2-2-22-2000000002i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22i−2i002i−2i00−2i2i00−2i2i000000−i2i2−i2i2i2−i2i2−i2−222−2−222−22−2−222−2−22000000000000000000000000
χ542222-2-2-2-2-2-222-2-22222-2-2-22-2000000002i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−2i2i00−2i2i002i−2i002i−2i000000−i2i2−i2i2i2−i2i2−i22−2−222−2−22−222−2−222−2000000000000000000000000
χ552222-2-2-2-2-2-222-2-22222-2-2-22-2000000002−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i22i−2i002i−2i00−2i2i00−2i2i000000i2−i2i2−i2−i2i2−i2i22−2−222−2−22−222−2−222−2000000000000000000000000
χ562222-2-2-2-2-2-222-2-22222-2-2-22-2000000002−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−2i2i00−2i2i002i−2i002i−2i000000i2−i2i2−i2−i2i2−i2i2−222−2−222−22−2−222−2−22000000000000000000000000
χ572222-2-2-2-2-2-222-2-222-2-2222-2200000000-2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2002-2002-200-2200-220000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ582222-2-2-2-2-2-222-2-222-2-2222-2200000000-2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200-2200-22002-2002-20000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ592222-2-2-2-2-2-222-2-222-2-2222-2200000000-2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2002-2002-200-2200-220000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ602222-2-2-2-2-2-222-2-222-2-2222-2200000000-2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200-2200-22002-2002-20000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ6122-2-222-2-222-2-2-2-2222-22-22-2-2000000002i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2002i−2i00−2i2i002i−2i00−2i2i0000i2−i2−i2i2i2−i2−i2i22−22−2−22−222−22−2−22−22000000000000000000000000
χ6222-2-222-2-222-2-2-2-2222-22-22-2-2000000002i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200−2i2i002i−2i00−2i2i002i−2i0000i2−i2−i2i2i2−i2−i2i2−22−222−22−2−22−222−22−2000000000000000000000000
χ6322-2-222-2-222-2-2-2-2222-22-22-2-2000000002−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2002i−2i00−2i2i002i−2i00−2i2i0000−i2i2i2−i2−i2i2i2−i2−22−222−22−2−22−222−22−2000000000000000000000000
χ6422-2-222-2-222-2-2-2-2222-22-22-2-2000000002−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200−2i2i002i−2i00−2i2i002i−2i0000−i2i2i2−i2−i2i2i2−i22−22−2−22−222−22−2−22−22000000000000000000000000
χ6522-2-222-2-222-2-2-2-222-22-22-22200000000-2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i22-200-22002-200-22000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.