Finite Group Databasebeta

← Group #197664

Character table — Group #197664

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222244444444444444444444444444444444444444444444444444444488888888161616161616161616161616
order12224444224444444444444422222244444444444444448888888888888888888888888888888888888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-111-1-1-1-11111111-111-1-11-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-1-1-11111111-111-1-11-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ1111111111-1-1-1-111-1-1-1-11111111-111-1-11-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111
χ1211111111-1-1-1-111-1-1-1-11111111-111-1-11-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11111-1-1
χ1311111111-1-1-1-111-1-1-1-11111111-1-1-1111-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-111
χ1411111111-1-1-1-111-1-1-1-11111111-1-1-1111-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-111-1-1
χ1511111111-1-1-1-111-1-1-1-11111111-1-1-1111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-111-1-1-1-11111111-1-1-1111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ171111-1-1-1-111-1-11111-1-111-1-1-1-1-1-111-1-111-1-1111-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1i−ii−i1-11-1
χ181111-1-1-1-111-1-11111-1-111-1-1-1-1-1-111-1-111-1-1111-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11−ii−ii-11-11
χ191111-1-1-1-111-1-11111-1-111-1-1-1-1-1-111-1-111-1-1111-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11i−ii−i-11-11
χ201111-1-1-1-111-1-11111-1-111-1-1-1-1-1-111-1-111-1-1111-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1−ii−ii1-11-1
χ211111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-11-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i1-11-1−ii−ii-11-11
χ221111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-11-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii-11-11i−ii−i1-11-1
χ231111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-11-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i-11-11−ii−ii1-11-1
χ241111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-11-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii1-11-1i−ii−i-11-11
χ251111-1-1-1-1-1-11111-1-11111-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11i−i−ii1-1-11
χ261111-1-1-1-1-1-11111-1-11111-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1−iii−i-111-1
χ271111-1-1-1-1-1-11111-1-11111-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1i−i−ii-111-1
χ281111-1-1-1-1-1-11111-1-11111-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11−iii−i1-1-11
χ291111-1-1-1-1-1-11111-1-11111-1-1-1-1-11-1-1-1-11-11111-11-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii1-1-11−iii−i-111-1
χ301111-1-1-1-1-1-11111-1-11111-1-1-1-1-11-1-1-1-11-11111-11-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-111-1i−i−ii1-1-11
χ311111-1-1-1-1-1-11111-1-11111-1-1-1-1-11-1-1-1-11-11111-11-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-111-1−iii−i1-1-11
χ321111-1-1-1-1-1-11111-1-11111-1-1-1-1-11-1-1-1-11-11111-11-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i1-1-11i−i−ii-111-1
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χ3422222222222222-2-2-2-2-2-2-2-222-2-20000-2-2000022000000000000000000000000-2-222-2-222-2-222-2-22200000000000000000000
χ35222222222222-2-222222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000000000000000
χ36222222222222-2-222222222-2-2-2-2-2-222-2-2-2-222-2-22222-2-2-2-20000000000000000000000000000000000000000000000000000
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χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-2220000220000-2-200000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ3922222222-2-2-2-2222222-2-2-2-222-220000-220000-2-200000000000000000000000022-2-222-2-2-2-222-2-22200000000000000000000
χ4022222222-2-2-2-2222222-2-2-2-222-220000-220000-2-2000000000000000000000000-2-222-2-22222-2-222-2-200000000000000000000
χ4122222222-2-2-2-2-2-22222-2-2-2-2-2-22-200002-2000022000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-22222-2-2-2-2-2-22-200002-200002200000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-22222-2-2-222222-22222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-22222-2-2-22-2-2-2-2-22-2-2-2-222222222220000000000000000000000000000000000000000000000000000
χ452222-2-2-2-222-2-222-2-222-2-222-2-2220000-2-200002-20000000000000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000
χ462222-2-2-2-222-2-222-2-222-2-222-2-2220000-2-200002-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000
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χ482222-2-2-2-222-2-2-2-222-2-222-2-22222-2-2-2-2-2-22222-2222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ492222-2-2-2-222-2-2-2-2-2-222-2-22222-2-20000220000-220000000022-2-2-2-22222-2-2-2-222000000000000000000000000000000000000
χ502222-2-2-2-222-2-2-2-2-2-222-2-22222-2-20000220000-2200000000-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000
χ512222-2-2-2-2-2-2222222-2-2-2-222-2-22-20000-220000-220000000000000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000
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χ542222-2-2-2-2-2-222-2-222-2-2-2-22222-2200002-200002-200000000-2-22222-2-222-2-2-2-222000000000000000000000000000000000000
χ552222-2-2-2-2-2-222-2-2-2-22222-2-2222-222-2-2-22-2-2222-2-2-222-2-2220000000000000000000000000000000000000000000000000000
χ562222-2-2-2-2-2-222-2-2-2-22222-2-2222-2-2-222-2222-2-22-222-2-222-2-20000000000000000000000000000000000000000000000000000
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χ582-22-22i2i−2i−2i2-22i−2i002-22i−2i2-22i−2i0000002-200002i−2i002i−2i2-20000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000
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χ672-22-22i2i−2i−2i-22−2i2i002-22i−2i-22−2i2i0000-220000−2i2i000000002-22i−2i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000000000000000
χ682-22-22i2i−2i−2i-22−2i2i002-22i−2i-22−2i2i0000-220000−2i2i000000002-22i−2i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000000000000000
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χ702-22-22i2i−2i−2i-22−2i2i00-22−2i2i2-22i−2i0000002-200002i−2i00−2i2i-220000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000
χ712-22-22i2i−2i−2i-22−2i2i00-22−2i2i2-22i−2i000000-220000−2i2i002i−2i2-200001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000
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χ742-22-2−2i−2i2i2i2-2−2i2i002-2−2i2i2-2−2i2i0000002-20000−2i2i00−2i2i2-20000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000
χ752-22-2−2i−2i2i2i2-2−2i2i002-2−2i2i2-2−2i2i000000-2200002i−2i002i−2i-2200001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000
χ762-22-2−2i−2i2i2i2-2−2i2i002-2−2i2i2-2−2i2i000000-2200002i−2i002i−2i-220000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000
χ772-22-2−2i−2i2i2i2-2−2i2i00-222i−2i-222i−2i00002-20000−2i2i000000002-2−2i2i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000000000
χ782-22-2−2i−2i2i2i2-2−2i2i00-222i−2i-222i−2i00002-20000−2i2i000000002-2−2i2i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000000000
χ792-22-2−2i−2i2i2i2-2−2i2i00-222i−2i-222i−2i0000-2200002i−2i00000000-222i−2i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000000000
χ802-22-2−2i−2i2i2i2-2−2i2i00-222i−2i-222i−2i0000-2200002i−2i00000000-222i−2i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000000000
χ812-22-2−2i−2i2i2i-222i−2i002-2−2i2i-222i−2i00002-20000−2i2i00000000-222i−2i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000000000
χ822-22-2−2i−2i2i2i-222i−2i002-2−2i2i-222i−2i00002-20000−2i2i00000000-222i−2i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000000000
χ832-22-2−2i−2i2i2i-222i−2i002-2−2i2i-222i−2i0000-2200002i−2i000000002-2−2i2i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000000000
χ842-22-2−2i−2i2i2i-222i−2i002-2−2i2i-222i−2i0000-2200002i−2i000000002-2−2i2i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000000000
χ852-22-2−2i−2i2i2i-222i−2i00-222i−2i2-2−2i2i0000002-20000−2i2i002i−2i-2200001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000
χ862-22-2−2i−2i2i2i-222i−2i00-222i−2i2-2−2i2i0000002-20000−2i2i002i−2i-220000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000
χ872-22-2−2i−2i2i2i-222i−2i00-222i−2i2-2−2i2i000000-2200002i−2i00−2i2i2-200001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000
χ882-22-2−2i−2i2i2i-222i−2i00-222i−2i2-2−2i2i000000-2200002i−2i00−2i2i2-20000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000
χ894-4-444i−4i4i−4i00004-4000000004i−4i00000000000000000000000000000000000000000000000000000000002−2i−2+2i2+2i−2−2i000000000000
χ904-4-444i−4i4i−4i00004-4000000004i−4i0000000000000000000000000000000000000000000000000000000000−2+2i2−2i−2−2i2+2i000000000000
χ914-4-444i−4i4i−4i0000-4400000000−4i4i0000000000000000000000000000000000000000000000000000002+2i−2−2i2−2i−2+2i0000000000000000
χ924-4-444i−4i4i−4i0000-4400000000−4i4i000000000000000000000000000000000000000000000000000000−2−2i2+2i−2+2i2−2i0000000000000000
χ934-4-44−4i4i−4i4i00004-400000000−4i4i00000000000000000000000000000000000000000000000000000000002+2i−2−2i2−2i−2+2i000000000000
χ944-4-44−4i4i−4i4i00004-400000000−4i4i0000000000000000000000000000000000000000000000000000000000−2−2i2+2i−2+2i2−2i000000000000
χ954-4-44−4i4i−4i4i0000-44000000004i−4i0000000000000000000000000000000000000000000000000000002−2i−2+2i2+2i−2−2i0000000000000000
χ964-4-44−4i4i−4i4i0000-44000000004i−4i000000000000000000000000000000000000000000000000000000−2+2i2−2i−2−2i2+2i0000000000000000
χ9788-8-88-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-888-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).