Finite Group Databasebeta

← Group #210751

Character table — Group #210751

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111111111111222222222222222222222222222222224444444444444444444444444444444444444444444488888888888888881616161616161616
order12222222444444444444444488888888888888888888888822444444888888888888888888888888888888888888444444448888888844448888
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
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ9111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ10111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ11111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ12111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ1711111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−i11111111-1-1-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i1-11-1i−ii−i
χ1811111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−i11111111-1-1-1-1-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-111-1-111−i−iii−i−iii-11-11−ii−ii
χ1911111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−i11111111-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii11-1-111-1-1ii−i−iii−i−i-11-11−ii−ii
χ2011111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−i11111111-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111-1-111−i−iii−i−iii1-11-1i−ii−i
χ2111111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-11111111111-1-111-1-1ii−i−iii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii1-1-11i−i−ii
χ2211111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-11111111111-1-111-1-1ii−i−iii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i-111-1−iii−i
χ2311111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-111111111-1-111-1-111ii−i−i−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i11-1-1-1-111ii−i−i−i−iii-111-1−iii−i
χ2411111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-111111111-1-111-1-111ii−i−i−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-11111-1-1−i−iiiii−i−i1-1-11i−i−ii
χ2511111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii11111111-1-1-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii1-11-1−ii−ii
χ2611111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii11111111-1-1-1-1-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i-11-11i−ii−i
χ2711111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i11-1-111-1-1−i−iii−i−iii-11-11i−ii−i
χ2811111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii11111111-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111-1-111ii−i−iii−i−i1-11-1−ii−ii
χ2911111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-11111111111-1-111-1-1−i−iii−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i1-1-11−iii−i
χ3011111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-11111111111-1-111-1-1−i−iii−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii-111-1i−i−ii
χ3111111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-111111111-1-111-1-111−i−iiiii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii11-1-1-1-111−i−iiiii−i−i-111-1i−i−ii
χ3211111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-111111111-1-111-1-111−i−iiiii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-11111-1-1ii−i−i−i−iii1-1-11−iii−i
χ332222222222222222-2-2-2-2-2-2-2-22222222200000000000000002222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-2-2-2222222220000000000000000-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-2222222222222-2-2-2-2000000000000000000000000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-2-2-222-2-2222i2i2i2i−2i−2i−2i−2i000000000000000022-2-2-2-222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-2-2-222-2-2222i2i2i2i−2i−2i−2i−2i0000000000000000-2-22222-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-222-2-222−2i−2i−2i−2i2i2i2i2i000000000000000022-2-2-2-2222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-222-2-222−2i−2i−2i−2i2i2i2i2i0000000000000000-2-22222-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ4122-2-22-22-22i−2i2i−2i2i−2i2i−2i000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3i2i2i2i2−i2−i2−i2−i22222−2−2−2−200002i−2i2-2000000002ζ3−2ζ32ζ−2ζ1−i1−i−1+i−1+i1+i1+i−1−i−1−i22−2−2i2i2−i2−i21+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000000000000000
χ4222-2-22-22-22i−2i2i−2i2i−2i2i−2i000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3i2i2i2i2−i2−i2−i2−i22222−2−2−2−20000−2i2i-2200000000−2ζ32ζ3−2ζ2ζ1−i1−i−1+i−1+i1+i1+i−1−i−1−i−2−222−i2−i2i2i2−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000000000000000
χ4322-2-22-22-22i−2i2i−2i2i−2i2i−2i000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3−i2−i2−i2−i2i2i2i2i2−2−2−2−2222200002i−2i2-2000000002ζ3−2ζ32ζ−2ζ−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2−222−i2−i2i2i2−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000000000000000
χ4422-2-22-22-22i−2i2i−2i2i−2i2i−2i000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3−i2−i2−i2−i2i2i2i2i2−2−2−2−222220000−2i2i-2200000000−2ζ32ζ3−2ζ2ζ−1+i−1+i1−i1−i−1−i−1−i1+i1+i22−2−2i2i2−i2−i21+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000000000000000
χ4522-2-22-22-22i−2i2i−2i2i−2i2i−2i00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3i2i2i2i2−i2−i2−i2−i22222−2−2−2−200002i−2i2-200000000−2ζ32ζ3−2ζ2ζ−1+i−1+i1−i1−i−1−i−1−i1+i1+i22−2−2i2i2−i2−i2−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000000000000000
χ4622-2-22-22-22i−2i2i−2i2i−2i2i−2i00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3i2i2i2i2−i2−i2−i2−i22222−2−2−2−20000−2i2i-22000000002ζ3−2ζ32ζ−2ζ−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2−222−i2−i2i2i21+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000000000000000
χ4722-2-22-22-22i−2i2i−2i2i−2i2i−2i00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3−i2−i2−i2−i2i2i2i2i2−2−2−2−2222200002i−2i2-200000000−2ζ32ζ3−2ζ2ζ1−i1−i−1+i−1+i1+i1+i−1−i−1−i−2−222−i2−i2i2i21+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000000000000000
χ4822-2-22-22-22i−2i2i−2i2i−2i2i−2i00000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3−i2−i2−i2−i2i2i2i2i2−2−2−2−222220000−2i2i-22000000002ζ3−2ζ32ζ−2ζ1−i1−i−1+i−1+i1+i1+i−1−i−1−i22−2−2i2i2−i2−i2−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000000000000000
χ4922-2-22-22-2−2i2i−2i2i−2i2i−2i2i000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζi2i2i2i2−i2−i2−i2−i2−2−2−2−2222200002i−2i-2200000000−2ζ2ζ−2ζ32ζ31+i1+i−1−i−1−i1−i1−i−1+i−1+i22−2−2−i2−i2i2i2−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000000000000000
χ5022-2-22-22-2−2i2i−2i2i−2i2i−2i2i000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζi2i2i2i2−i2−i2−i2−i2−2−2−2−222220000−2i2i2-2000000002ζ−2ζ2ζ3−2ζ31+i1+i−1−i−1−i1−i1−i−1+i−1+i−2−222i2i2−i2−i21−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000000000000000
χ5122-2-22-22-2−2i2i−2i2i−2i2i−2i2i000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ−i2−i2−i2−i2i2i2i2i22222−2−2−2−200002i−2i-2200000000−2ζ2ζ−2ζ32ζ3−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2−222i2i2−i2−i21−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000000000000000
χ5222-2-22-22-2−2i2i−2i2i−2i2i−2i2i000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ−i2−i2−i2−i2i2i2i2i22222−2−2−2−20000−2i2i2-2000000002ζ−2ζ2ζ3−2ζ3−1−i−1−i1+i1+i−1+i−1+i1−i1−i22−2−2−i2−i2i2i2−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000000000000000
χ5322-2-22-22-2−2i2i−2i2i−2i2i−2i2i00000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζi2i2i2i2−i2−i2−i2−i2−2−2−2−2222200002i−2i-22000000002ζ−2ζ2ζ3−2ζ3−1−i−1−i1+i1+i−1+i−1+i1−i1−i22−2−2−i2−i2i2i21−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000000000000000
χ5422-2-22-22-2−2i2i−2i2i−2i2i−2i2i00000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζi2i2i2i2−i2−i2−i2−i2−2−2−2−222220000−2i2i2-200000000−2ζ2ζ−2ζ32ζ3−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2−222i2i2−i2−i2−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000000000000000
χ5522-2-22-22-2−2i2i−2i2i−2i2i−2i2i00000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ−i2−i2−i2−i2i2i2i2i22222−2−2−2−200002i−2i-22000000002ζ−2ζ2ζ3−2ζ31+i1+i−1−i−1−i1−i1−i−1+i−1+i−2−222i2i2−i2−i2−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000000000000000
χ5622-2-22-22-2−2i2i−2i2i−2i2i−2i2i00000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ−i2−i2−i2−i2i2i2i2i22222−2−2−2−20000−2i2i2-200000000−2ζ2ζ−2ζ32ζ31+i1+i−1−i−1−i1−i1−i−1+i−1+i22−2−2−i2−i2i2i21−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000000000000000
χ5722-2-2-22-222i−2i−2i2i−2i2i2i−2i2-22i−2i2-22i−2i000000002i2i−2i−2i2i2i−2i−2i22-2-222-2-200000000000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ300000000
χ5822-2-2-22-222i−2i−2i2i−2i2i2i−2i2-22i−2i2-22i−2i000000002i2i−2i−2i2i2i−2i−2i22-2-222-2-20000000000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ300000000
χ5922-2-2-22-222i−2i−2i2i−2i2i2i−2i2-22i−2i2-22i−2i00000000−2i−2i2i2i−2i−2i2i2i-2-222-2-22200000000000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ300000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.