Finite Group Databasebeta

← Group #110816

Character table — Group #110816

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111111111111222222222222222222222222222222224444444444444444444444444444444444444444444488888888888888881616161616161616
order12222222444444444444444444444444888888888888888822448888888888888888888888888888888888888888888888888888888844444444
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
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111
χ171-1-11-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-111-1-111-1-1ii−i−iii−i−ii−ii−i1-11-1
χ181-1-11-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-1-1-111-1-111−i−iii−i−iii−ii−ii-11-11
χ191-1-11-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-1-1-11111-1-1-1-1111111-1-111-1-1ii−i−iii−i−i−ii−ii-11-11
χ201-1-11-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-1-1-11111-1-1-1-11111-1-111-1-111−i−iii−i−iiii−ii−i1-11-1
χ211-1-11-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-1-1-11111-1-1-1-1111111-1-111-1-1−i−iii−i−iiii−ii−i-11-11
χ221-1-11-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-1-1-11111-1-1-1-11111-1-111-1-111ii−i−iii−i−i−ii−ii1-11-1
χ231-1-11-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1111-1-1-1-11111-1-1-1-111-1-111-1-1−i−iii−i−iii−ii−ii1-11-1
χ241-1-11-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1111-1-1-1-11111-1-1-1-1-1-111-1-111ii−i−iii−i−ii−ii−i-11-11
χ251-1-11-1-111-1-1-1-111111111-1-111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-111-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-1-11111-1-1−iii−i-111-1
χ261-1-11-1-111-1-1-1-111111111-1-111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-111-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i11-1-1-1-111i−i−ii1-1-11
χ271-1-11-1-111-1-1-1-111111111-1-111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-111-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-1-11111-1-1i−i−ii1-1-11
χ281-1-11-1-111-1-1-1-111111111-1-111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-111-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i11-1-1-1-111−iii−i-111-1
χ291-1-11-1-111-1-1-1-111111111-1-111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-111-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii11-1-1-1-111−iii−i1-1-11
χ301-1-11-1-111-1-1-1-111111111-1-111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-111-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-1-11111-1-1i−i−ii-111-1
χ311-1-11-1-111-1-1-1-111111111-1-111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii11-1-1-1-111i−i−ii-111-1
χ321-1-11-1-111-1-1-1-111111111-1-111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-1-11111-1-1−iii−i1-1-11
χ33222222222222222222-2-222-2-2-2-222-2-2220000000000000000-2-2-2-222-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ34222222222222222222-2-222-2-2-2-222-2-2220000000000000000-2-2-2-2-2-222-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ352222222222222222-2-222-2-22222-2-222-2-22222222222222222-2-2-2-20000000000000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ362222222222222222-2-222-2-22222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000222222220000000000000000000000000000000000000000
χ372222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022220000000000000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ382222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222000000000000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-222-2-2000000000000000022-2-22i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-222-2-2000000000000000022-2-2−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-22222222222-2-2-2-2-2-2-2-222-2-20000000000000000-2-2-2-222220000000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-222-2-2-2-2-2-2-2-22222222222-2-200000000000000002222-2-2-2-20000000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22222220000000000000000-2-22200000000000000000000000022-2-222-2-2-2-222-2-222000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22222220000000000000000-2-222000000000000000000000000-2-222-2-22222-2-222-2-2000000000000000000000000
χ4522-2-22-22-22i2i−2i−2i2i2i−2i−2i002-2002i−2i2-2002i−2i0022-2-222-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ4622-2-22-22-22i2i−2i−2i2i2i−2i−2i002-2002i−2i2-2002i−2i0022-2-222-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ4722-2-22-22-22i2i−2i−2i2i2i−2i−2i002-2002i−2i2-2002i−2i00-2-222-2-222−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ4822-2-22-22-22i2i−2i−2i2i2i−2i−2i002-2002i−2i2-2002i−2i00-2-222-2-222−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ4922-2-22-22-2−2i−2i2i2i−2i−2i2i2i002-200−2i2i2-200−2i2i0022-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ5022-2-22-22-2−2i−2i2i2i−2i−2i2i2i002-200−2i2i2-200−2i2i0022-2-222-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ5122-2-22-22-2−2i−2i2i2i−2i−2i2i2i002-200−2i2i2-200−2i2i00-2-222-2-2222i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
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χ5422-2-2-22-222i−2i2i−2i2i−2i2i−2i2-2002-200002i−2i002i−2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i2000000−2ζ32ζ300−2ζ32ζ300−2ζ2ζ00−2ζ2ζ2−22−2i2−i2i2−i2−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i000000000000000000000000
χ5522-2-2-22-222i−2i2i−2i2i−2i2i−2i2-2002-200002i−2i002i−2i−22−22−22−22−i2i2−i2i2−i2i2−i2i20000002ζ3−2ζ3002ζ3−2ζ3002ζ−2ζ002ζ−2ζ−22−22−i2i2−i2i2−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i000000000000000000000000
χ5622-2-2-22-222i−2i2i−2i2i−2i2i−2i2-2002-200002i−2i002i−2i−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000−2ζ32ζ300−2ζ32ζ300−2ζ2ζ00−2ζ2ζ−22−22−i2i2−i2i21−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i000000000000000000000000
χ5722-2-2-22-222i−2i2i−2i2i−2i2i−2i-2200-220000−2i2i00−2i2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i200002ζ−2ζ002ζ−2ζ002ζ3−2ζ3002ζ3−2ζ300−22−22−i2i2−i2i21+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i000000000000000000000000
χ5822-2-2-22-222i−2i2i−2i2i−2i2i−2i-2200-220000−2i2i00−2i2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i20000−2ζ2ζ00−2ζ2ζ00−2ζ32ζ300−2ζ32ζ300−22−22−i2i2−i2i2−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i000000000000000000000000
χ5922-2-2-22-222i−2i2i−2i2i−2i2i−2i-2200-220000−2i2i00−2i2i−22−22−22−22−i2i2−i2i2−i2i2−i2i200002ζ−2ζ002ζ−2ζ002ζ3−2ζ3002ζ3−2ζ3002−22−2i2−i2i2−i2−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i000000000000000000000000
χ6022-2-2-22-222i−2i2i−2i2i−2i2i−2i-2200-220000−2i2i00−2i2i−22−22−22−22−i2i2−i2i2−i2i2−i2i20000−2ζ2ζ00−2ζ2ζ00−2ζ32ζ300−2ζ32ζ3002−22−2i2−i2i2−i21+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.