Finite Group Databasebeta

← Group #364009

Character table — Group #364009

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12222222222222224444444444444444444444444444444444444444222244444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ91111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ101111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ121111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ131111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ141111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ151111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ161111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ171-1-1-1-11111-1-1-1-11111111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ181-1-1-1-11111-1-1-1-11111111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ191-1-1-1-11111-1-1-1-11111111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-111ii−i−iii−i−iii−i−iii−i−i-1-111-1-111-1-111−i−iii−i−iii−i−iii−i−iii
χ201-1-1-1-11111-1-1-1-11111111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-111−i−iii−i−iii−i−iii−i−iii-1-111-1-111-1-111ii−i−iii−i−iii−i−iii−i−i
χ211-1-1-1-11111-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1ii−i−iii−i−i−i−iii−i−iii11-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ221-1-1-1-11111-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1−i−iii−i−iiiii−i−iii−i−i11-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ231-1-1-1-11111-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i
χ241-1-1-1-11111-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii
χ251-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ261-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ271-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ281-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ291-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1ii−i−i−i−iii−i−iiiii−i−i-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ301-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1−i−iiiii−i−iii−i−i−i−iii-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ311-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i11-1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii
χ321-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii11-1-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i
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χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-2000000000000000000000000000000000000000000000000
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χ38222-2-222-2-222-2-22-2-200000022-2-222-2-22i2i−2i−2i2i2i−2i−2i0000002i−2i2i−2i0000000000000000000000000000000000000000−22−22−22−22−i2i2−i2i2−i2i2−i2i2
χ39222-2-222-2-222-2-22-2-200000022-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000−2i2i−2i2i00000000000000000000000000000000000000002−22−22−22−2−i2i2−i2i2−i2i2−i2i2
χ40222-2-222-2-222-2-22-2-200000022-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000−2i2i−2i2i0000000000000000000000000000000000000000−22−22−22−22i2−i2i2−i2i2−i2i2−i2
χ41222-2-222-2-222-2-22-2-2000000-2-222-2-2222i2i−2i−2i2i2i−2i−2i000000−2i2i−2i2i00000000000000000000000000000000000000002−22−2−22−22i2−i2i2−i2−i2i2−i2i2
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χ45222-2-22-22-2-2-222-22-222-2-22-2000000002i−2i2i−2i2i−2i2i−2i2-22i−2i2i−2i000000000000000000002i−2i2i−2i00002-22-20000000000000000000000000000
χ46222-2-22-22-2-2-222-22-222-2-22-2000000002i−2i2i−2i2i−2i2i−2i2-22i−2i2i−2i00000000000000000000−2i2i−2i2i0000-22-220000000000000000000000000000
χ47222-2-22-22-2-2-222-22-222-2-22-200000000−2i2i−2i2i−2i2i−2i2i2-2−2i2i−2i2i000000000000000000002i−2i2i−2i0000-22-220000000000000000000000000000
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χ51222-2-22-22-2-2-222-22-2-2-222-2200000000−2i2i−2i2i−2i2i−2i2i-222i−2i2i−2i00000000000000002i−2i2i−2i0000-22-2200000000000000000000000000000000
χ52222-2-22-22-2-2-222-22-2-2-222-2200000000−2i2i−2i2i−2i2i−2i2i-222i−2i2i−2i0000000000000000−2i2i−2i2i00002-22-200000000000000000000000000000000
χ5322-22-2-222-22-22-2-2-222-22-22-22i−2i2i−2i2i−2i2i−2i00000000-22000000002i−2i2i−2i00000000000000000000000000002-22-22i−2i2i−2i0000000000000000
χ5422-22-2-222-22-22-2-2-222-22-22-22i−2i2i−2i2i−2i2i−2i00000000-22000000002i−2i2i−2i0000000000000000000000000000-22-22−2i2i−2i2i0000000000000000
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χ672-22-22-222-2-22-22-2-22-22-222-2−2i2i−2i2i2i−2i2i−2i00000000-22000000002i−2i−2i2i00002-2-220000000000000000−2i2i2i−2i000000000000000000000000
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χ722-2-22222-2-2-2-2222-2-200000022-2-2-2-222−2i−2i2i2i2i2i−2i−2i000000−2i2i2i−2i0000000000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2−222−2−222−2
χ732-2-22222-2-2-2-2222-2-2000000-2-22222-2-22i2i−2i−2i−2i−2i2i2i000000−2i2i2i−2i0000000000000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2−222−22−2−22
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χ762-2-22222-2-2-2-2222-2-2000000-2-22222-2-2−2i−2i2i2i2i2i−2i−2i0000002i−2i−2i2i0000000000000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2−222−22−2−22
χ772-2-2222-22-222-2-2-22-222-2-2-22000000002i−2i2i−2i−2i2i−2i2i-222i−2i−2i2i000000000000000000002-2-220000−2i2i2i−2i0000000000000000000000000000
χ782-2-2222-22-222-2-2-22-222-2-2-22000000002i−2i2i−2i−2i2i−2i2i-222i−2i−2i2i00000000000000000000-222-200002i−2i−2i2i0000000000000000000000000000
χ792-2-2222-22-222-2-2-22-222-2-2-2200000000−2i2i−2i2i2i−2i2i−2i-22−2i2i2i−2i000000000000000000002-2-2200002i−2i−2i2i0000000000000000000000000000
χ802-2-2222-22-222-2-2-22-222-2-2-2200000000−2i2i−2i2i2i−2i2i−2i-22−2i2i2i−2i00000000000000000000-222-20000−2i2i2i−2i0000000000000000000000000000
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χ862-2-2-2-22222-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-2-2-222222222-2-2-2-222-2-22222-2-2000000000000000000000000000000000000000000000000
χ872-2-2-2-22222-2-2-2-2222-2-2-2-222-2-2-2-222222222-2-2-2-222-2-222-2-22222-2-222-2-2000000000000000000000000000000000000000000000000
χ882-2-2-2-22222-2-2-2-2222-2-2-2-222-2-2-2-22222-2-2-2-222222222-2-222-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ89444444-4-44-4-4-4-4-4-44000000000000004-4-444-4-44000000000000000000000000000000000000000000000000000000000000000000
χ90444444-4-44-4-4-4-4-4-4400000000000000-444-4-444-4000000000000000000000000000000000000000000000000000000000000000000
χ9144-44-4-4-4-4-4-44-444440000000000000000000000000000000000004-44-4000000000000000000000000000000000000000000000000
χ9244-44-4-4-4-4-4-44-44444000000000000000000000000000000000000-44-44000000000000000000000000000000000000000000000000
χ9344-4-44-44-444-4-44-44-40000004i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000000000
χ9444-4-44-44-444-4-44-44-4000000−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000000000
χ9544-4-44-4-444-444-44-4-44-4-44440000000000000000-4-40000000000000000000000000000000000000000000000000000000000000000
χ9644-4-44-4-444-444-44-4-4-444-4-4-40000000000000000440000000000000000000000000000000000000000000000000000000000000000
χ974-444-4-44-44-444-4-44-40000004i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000000000
χ984-444-4-44-44-444-4-44-4000000−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000000000
χ994-444-4-4-4444-4-444-4-44-4-44-4-40000000000000000440000000000000000000000000000000000000000000000000000000000000000
χ1004-444-4-4-4444-4-444-4-4-444-4440000000000000000-4-40000000000000000000000000000000000000000000000000000000000000000
χ1014-44-44-4-4-4-44-44-44440000000000000000000000000000000000004-4-44000000000000000000000000000000000000000000000000
χ1024-44-44-4-4-4-44-44-4444000000000000000000000000000000000000-444-4000000000000000000000000000000000000000000000000
χ1034-4-4-4-44-4-444444-4-44000000000000004-4-44-444-4000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-4-44-4-444444-4-4400000000000000-444-44-4-44000000000000000000000000000000000000000000000000000000000000000000

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