Finite Group Databasebeta

← Group #164366

Character table — Group #164366

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11111111222222222222222222224444444444444444444444444444448888888888888888888888888888888161616161616
order12222222444444444444444444442222444444444488888888888888884444444888888888888888888888888444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1-11
χ611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii111-1-111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1111-1
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i111-1-111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1-11
χ9111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111111111111111111-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-11-1-11
χ10111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-11111-111-1
χ11111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111-1-111-111-1
χ12111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111111-1-111-1-111-1-111-1-111-1-11-1-11
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−i1-1-111-1-1−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iii-1-1-1111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii1-1-1-1-111−i−iiiii−i−iii−i−i−i−iii−i−iiiii−i−i111-1-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i1-1-1-1-111ii−i−i−i−iii−i−iiiii−i−iii−i−i−i−iii111-1-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiii1-1-111-1-1ii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−i-1-1-1111
χ1711111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-11111-1-11111111111111111-11-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-11-1-1
χ1811111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-111-111
χ1911111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-111-111
χ2011111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-111111111111111-1-111-1-11-1-11-1-1
χ2111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111iiii−i−i−i−iiiii−i−i−i−i-11-111-1-1ii−i−i−i−iii−i−i−i−iiiii−i−iiiii−i−i1-11-11-1
χ2211111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111iiii−i−i−i−i−i−i−i−iiiii-11-1-1-111ii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−iii-11-11-11
χ2311111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111−i−i−i−iiiiiiiii−i−i−i−i-11-1-1-111−i−iii−i−iiiiiii−i−i−i−i−i−iiiii−i−i-11-11-11
χ2411111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111−i−i−i−iiiii−i−i−i−iiiii-11-111-1-1−i−iiiii−i−iiiii−i−i−i−iii−i−i−i−iii1-11-11-1
χ2511111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-111-1-1111111111111111111-1-111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-11-1-11-1
χ2611111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111111-111-11
χ2711111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-11-111-11
χ2811111111-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-111-1-111111111-11-1-11-1
χ2911111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1111-1-1−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iiiii-1111-1-1
χ3011111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11-1-111−i−iii−i−iii−i−iiiii−i−iiiii−i−i−i−i1-1-1-111
χ3111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11-1-111ii−i−iii−i−iii−i−i−i−iii−i−i−i−iiiii1-1-1-111
χ3211111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1111-1-1ii−i−i−i−iiiii−i−i−i−iiiiiii−i−i−i−i-1111-1-1
χ332222222222222222222222-2-222-2-222-2-222-2-2-2-2-2-2220000000000000000-2-2-20000000000000000000000000000000000
χ3422222222222222222222-2-222-2-222-2-222-2-222-2-222-2-20000000000000000-2-2-20000000000000000000000000000000000
χ35222222222222-2-2-2-2-2-2-2-222-2-222-2-2-2-22222-2-2-2-222-2-20000000000000000-2220000000000000000000000000000000000
χ36222222222222-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-222-2-2-2-2220000000000000000-2220000000000000000000000000000000000
χ3722222222-2-2-2-22222-2-2-2-222-2-222-2-22222-2-222-2-2-2-2-2-200000000000000002-220000000000000000000000000000000000
χ3822222222-2-2-2-22222-2-2-2-2-2-222-2-222-2-2-2-222-2-2-2-2222200000000000000002-220000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2222222-2-222-2-2-2-2-2-2-2-222-2-22222000000000000000022-20000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-22222-2-222-2-222222222-2-2-2-2-2-2-2-2000000000000000022-20000000000000000000000000000000000
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χ452-222-2-2-22000000000000−2i2i−2i2i−2i2i−2i2i000000002-200002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000−2i2i2-2000000000000000000000000000000
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χ522-22-222-2-22i2i−2i−2i22-2-22i2i−2i−2i00−2i2i002i−2i00-2200-2200−2i2i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000001−i−1+i1+i−1−i000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i000000
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χ552-22-222-2-22i2i−2i−2i-2-222−2i−2i2i2i00−2i2i002i−2i002-200-22002i−2i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000001−i−1+i1+i−1−i00000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000
χ562-22-222-2-22i2i−2i−2i-2-222−2i−2i2i2i00−2i2i002i−2i002-200-22002i−2i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000−1+i1−i−1−i1+i000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i000000
χ572-22-222-2-2−2i−2i2i2i22-2-2−2i−2i2i2i002i−2i00−2i2i00-2200-22002i−2i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000−1−i1+i−1+i1−i00000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i000000
χ582-22-222-2-2−2i−2i2i2i22-2-2−2i−2i2i2i002i−2i00−2i2i00-2200-22002i−2i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000001+i−1−i1−i−1+i000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i000000
χ592-22-222-2-2−2i−2i2i2i22-2-2−2i−2i2i2i00−2i2i002i−2i002-2002-200−2i2i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000001−i−1+i1+i−1−i000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i000000
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χ612-22-222-2-2−2i−2i2i2i-2-2222i2i−2i−2i002i−2i00−2i2i002-200-2200−2i2i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000001+i−1−i1−i−1+i00000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000
χ622-22-222-2-2−2i−2i2i2i-2-2222i2i−2i−2i002i−2i00−2i2i002-200-2200−2i2i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000−1−i1+i−1+i1−i000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i000000
χ632-22-222-2-2−2i−2i2i2i-2-2222i2i−2i−2i00−2i2i002i−2i00-22002-2002i−2i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000−1+i1−i−1−i1+i000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i000000
χ642-22-222-2-2−2i−2i2i2i-2-2222i2i−2i−2i00−2i2i002i−2i00-22002-2002i−2i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000001−i−1+i1+i−1−i00000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i000000
χ652-2-222-22-22i−2i2i−2i2i−2i2i−2i2-22-22i−2i00−2i2i002-2002-20000002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000001−i−1+i1+i−1−i00001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000000000
χ662-2-222-22-22i−2i2i−2i2i−2i2i−2i2-22-22i−2i00−2i2i002-2002-20000002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000−1+i1−i−1−i1+i0000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000000000
χ672-2-222-22-22i−2i2i−2i2i−2i2i−2i2-22-2−2i2i002i−2i00-2200-22000000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000−1−i1+i−1+i1−i0000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00000000000000
χ682-2-222-22-22i−2i2i−2i2i−2i2i−2i2-22-2−2i2i002i−2i00-2200-22000000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000001+i−1−i1−i−1+i00001+i−1−i−1+i1−i1−i−1+i−1−i1+i00000000000000
χ692-2-222-22-22i−2i2i−2i−2i2i−2i2i-22-222i−2i00−2i2i00-22002-2000000−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000−1+i1−i−1−i1+i00001−i−1+i−1−i1+i1+i−1−i−1+i1−i00000000000000
χ702-2-222-22-22i−2i2i−2i−2i2i−2i2i-22-222i−2i00−2i2i00-22002-2000000−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000001−i−1+i1+i−1−i0000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00000000000000
χ712-2-222-22-22i−2i2i−2i−2i2i−2i2i-22-22−2i2i002i−2i002-200-220000002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000001+i−1−i1−i−1+i0000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000000000
χ722-2-222-22-22i−2i2i−2i−2i2i−2i2i-22-22−2i2i002i−2i002-200-220000002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000−1−i1+i−1+i1−i00001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000000000
χ732-2-222-22-2−2i2i−2i2i2i−2i2i−2i-22-222i−2i00−2i2i002-200-22000000−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000001−i−1+i1+i−1−i0000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000000000
χ742-2-222-22-2−2i2i−2i2i2i−2i2i−2i-22-222i−2i00−2i2i002-200-22000000−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000−1+i1−i−1−i1+i00001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000000000
χ752-2-222-22-2−2i2i−2i2i2i−2i2i−2i-22-22−2i2i002i−2i00-22002-20000002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000−1−i1+i−1+i1−i00001+i−1−i−1+i1−i1−i−1+i−1−i1+i00000000000000
χ762-2-222-22-2−2i2i−2i2i2i−2i2i−2i-22-22−2i2i002i−2i00-22002-20000002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000001+i−1−i1−i−1+i0000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00000000000000
χ772-2-222-22-2−2i2i−2i2i−2i2i−2i2i2-22-22i−2i00−2i2i00-2200-220000002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000−1+i1−i−1−i1+i0000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00000000000000
χ782-2-222-22-2−2i2i−2i2i−2i2i−2i2i2-22-22i−2i00−2i2i00-2200-220000002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000001−i−1+i1+i−1−i00001−i−1+i−1−i1+i1+i−1−i−1+i1−i00000000000000
χ792-2-222-22-2−2i2i−2i2i−2i2i−2i2i2-22-2−2i2i002i−2i002-2002-2000000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000001+i−1−i1−i−1+i00001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000000000
χ802-2-222-22-2−2i2i−2i2i−2i2i−2i2i2-22-2−2i2i002i−2i002-2002-2000000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000−1−i1+i−1+i1−i0000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000000000
χ81444-4-4-44-4000000000000004400-4-4000000000000000000000022−22−2222−222222−220000000000000000000000000000000000000
χ82444-4-4-44-4000000000000004400-4-40000000000000000000000−222222−2222−22−22220000000000000000000000000000000000000
χ83444-4-4-44-400000000000000-4-4004400000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000
χ84444-4-4-44-400000000000000-4-400440000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000
χ8544-44-44-4-40000000000004400-4-4000000000000000022−22−2222−222222−22000000000000000000000000000000000000000000000
χ8644-44-44-4-40000000000004400-4-40000000000000000−222222−2222−22−2222000000000000000000000000000000000000000000000
χ8744-44-44-4-4000000000000-4-4004400000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000000
χ8844-44-44-4-4000000000000-4-400440000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000000
χ8944-4-44-4-444-4-444i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ9044-4-44-4-444-4-44−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ9144-4-44-4-44-444-44i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ9244-4-44-4-44-444-4−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000
χ934-444-4-4-440000000000004i−4i−4i4i4i−4i−4i4i00000000-44000000000000000000000000000000000000000000000000000000000
χ944-444-4-4-44000000000000−4i4i4i−4i−4i4i4i−4i00000000-44000000000000000000000000000000000000000000000000000000000
χ958-8-8-8-8888000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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