Finite Group Databasebeta

← Group #368447

Character table — Group #368447

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111111111111222222222222222222222222222222224444444444444444444444444444444444444444444488888888888888881616161616161616
order12222222444444442222222244444444888888888888888822444444444444444444888888888888888888888888444444448888888824448888
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
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ9111111111111111111-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1111-1-1
χ10111111111111111111-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-1-111
χ11111111111111111111-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-111-1-1-111
χ12111111111111111111-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111-1-1111-1-1
χ13111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-111-111-1-1
χ14111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11-1-11-1-111
χ15111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11-1-111
χ16111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-111-1-1
χ1711111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i-1-111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-111-1-111-1-1ii−i−iii−i−i11-1-1i−ii−i
χ1811111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i-1-111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1-1-111-1-111−i−iii−i−iii-1-111−ii−ii
χ1911111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-1-1-1111111-1-111-1-1ii−i−iii−i−i-1-111−ii−ii
χ2011111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-1-1-1-11111-1-111-1-111−i−iii−i−iii11-1-1i−ii−i
χ2111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-1-1-1111111-1-111-1-1−i−iii−i−iii-1-111i−ii−i
χ2211111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-1-1-11111-1-111-1-111ii−i−iii−i−i11-1-1−ii−ii
χ2311111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii-1-111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-111-1-111-1-1−i−iii−i−iii11-1-1−ii−ii
χ2411111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii-1-111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1-1-111-1-111ii−i−iii−i−i-1-111i−ii−i
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i11-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-1-1-1111111-1-1-1-111ii−i−i−i−iii1-11-1i−i−ii
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i11-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111-1-11111-1-1−i−iiiii−i−i-11-11−iii−i
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i11-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-111-1-1-1-111ii−i−i−i−iii-11-11−iii−i
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i11-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1-1-11111-1-1−i−iiiii−i−i1-11-1i−i−ii
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii11-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-111-1-1-1-111−i−iiiii−i−i-11-11i−i−ii
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii11-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1-1-11111-1-1ii−i−i−i−iii1-11-1−iii−i
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-1111111-1-1-1-111−i−iiiii−i−i1-11-1−iii−i
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111-1-11111-1-1ii−i−i−i−iii-11-11i−i−ii
χ332222222222222222-2-22222-2-2-2-22222-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000022-2-222-2-20000000000000000000000000000000000000000
χ342222222222222222-2-22222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000-2-222-2-2220000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222220000000000000000-2-222-2-2220000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222222000000000000000022-2-222-2-20000000000000000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i22-2-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i22-2-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-222-2-2-2-222-2-22222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-222-2-2-2-222-2-22222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i-2-22200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ4122-22-22-2-22i−2i2i2i−2i−2i2i−2i0022-2-200002i2i−2i−2i0000002ζ32ζ3−2ζ3−2ζ300002ζ2ζ−2ζ−2ζ00001+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i002ζ3−2ζ3002ζ−2ζi2i2−i2−i222−2−2i2i2−i2−i222−2−2000000000000000000000000
χ4222-22-22-2-22i−2i2i2i−2i−2i2i−2i0022-2-200002i2i−2i−2i0000002ζ32ζ3−2ζ3−2ζ300002ζ2ζ−2ζ−2ζ0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i002ζ3−2ζ3002ζ−2ζ−i2−i2i2i2−2−222−i2−i2i2i2−2−222000000000000000000000000
χ4322-22-22-2-22i−2i2i2i−2i−2i2i−2i0022-2-200002i2i−2i−2i000000−2ζ3−2ζ32ζ32ζ30000−2ζ−2ζ2ζ2ζ00001+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00−2ζ32ζ300−2ζ2ζ−i2−i2i2i2−2−222−i2−i2i2i2−2−222000000000000000000000000
χ4422-22-22-2-22i−2i2i2i−2i−2i2i−2i0022-2-200002i2i−2i−2i000000−2ζ3−2ζ32ζ32ζ30000−2ζ−2ζ2ζ2ζ0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00−2ζ32ζ300−2ζ2ζi2i2−i2−i222−2−2i2i2−i2−i222−2−2000000000000000000000000
χ4522-22-22-2-22i−2i2i2i−2i−2i2i−2i00-2-2220000−2i−2i2i2i0000002ζ32ζ3−2ζ3−2ζ300002ζ2ζ−2ζ−2ζ00001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00−2ζ32ζ300−2ζ2ζi2i2−i2−i222−2−2−i2−i2i2i2−2−222000000000000000000000000
χ4622-22-22-2-22i−2i2i2i−2i−2i2i−2i00-2-2220000−2i−2i2i2i0000002ζ32ζ3−2ζ3−2ζ300002ζ2ζ−2ζ−2ζ0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00−2ζ32ζ300−2ζ2ζ−i2−i2i2i2−2−222i2i2−i2−i222−2−2000000000000000000000000
χ4722-22-22-2-22i−2i2i2i−2i−2i2i−2i00-2-2220000−2i−2i2i2i000000−2ζ3−2ζ32ζ32ζ30000−2ζ−2ζ2ζ2ζ00001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i002ζ3−2ζ3002ζ−2ζ−i2−i2i2i2−2−222i2i2−i2−i222−2−2000000000000000000000000
χ4822-22-22-2-22i−2i2i2i−2i−2i2i−2i00-2-2220000−2i−2i2i2i000000−2ζ3−2ζ32ζ32ζ30000−2ζ−2ζ2ζ2ζ0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i002ζ3−2ζ3002ζ−2ζi2i2−i2−i222−2−2−i2−i2i2i2−2−222000000000000000000000000
χ4922-22-22-2-2−2i2i−2i−2i2i2i−2i2i0022-2-20000−2i−2i2i2i0000002ζ2ζ−2ζ−2ζ00002ζ32ζ3−2ζ3−2ζ300001−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i002ζ−2ζ002ζ3−2ζ3i2i2−i2−i2−2−222i2i2−i2−i2−2−222000000000000000000000000
χ5022-22-22-2-2−2i2i−2i−2i2i2i−2i2i0022-2-20000−2i−2i2i2i0000002ζ2ζ−2ζ−2ζ00002ζ32ζ3−2ζ3−2ζ30000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i002ζ−2ζ002ζ3−2ζ3−i2−i2i2i222−2−2−i2−i2i2i222−2−2000000000000000000000000
χ5122-22-22-2-2−2i2i−2i−2i2i2i−2i2i0022-2-20000−2i−2i2i2i000000−2ζ−2ζ2ζ2ζ0000−2ζ3−2ζ32ζ32ζ300001−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00−2ζ2ζ00−2ζ32ζ3−i2−i2i2i222−2−2−i2−i2i2i222−2−2000000000000000000000000
χ5222-22-22-2-2−2i2i−2i−2i2i2i−2i2i0022-2-20000−2i−2i2i2i000000−2ζ−2ζ2ζ2ζ0000−2ζ3−2ζ32ζ32ζ30000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00−2ζ2ζ00−2ζ32ζ3i2i2−i2−i2−2−222i2i2−i2−i2−2−222000000000000000000000000
χ5322-22-22-2-2−2i2i−2i−2i2i2i−2i2i00-2-22200002i2i−2i−2i0000002ζ2ζ−2ζ−2ζ00002ζ32ζ3−2ζ3−2ζ300001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00−2ζ2ζ00−2ζ32ζ3i2i2−i2−i2−2−222−i2−i2i2i222−2−2000000000000000000000000
χ5422-22-22-2-2−2i2i−2i−2i2i2i−2i2i00-2-22200002i2i−2i−2i0000002ζ2ζ−2ζ−2ζ00002ζ32ζ3−2ζ3−2ζ30000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00−2ζ2ζ00−2ζ32ζ3−i2−i2i2i222−2−2i2i2−i2−i2−2−222000000000000000000000000
χ5522-22-22-2-2−2i2i−2i−2i2i2i−2i2i00-2-22200002i2i−2i−2i000000−2ζ−2ζ2ζ2ζ0000−2ζ3−2ζ32ζ32ζ300001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i002ζ−2ζ002ζ3−2ζ3−i2−i2i2i222−2−2i2i2−i2−i2−2−222000000000000000000000000
χ5622-22-22-2-2−2i2i−2i−2i2i2i−2i2i00-2-22200002i2i−2i−2i000000−2ζ−2ζ2ζ2ζ0000−2ζ3−2ζ32ζ32ζ30000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i002ζ−2ζ002ζ3−2ζ3i2i2−i2−i2−2−222−i2−i2i2i222−2−2000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.