Finite Group Databasebeta

← Group #203166

Character table — Group #203166

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222244444444444444444444444444444444444444444444444444444488888888161616161616161616161616
order12224444222222444444444444444488888888888888888888888888888888888888888888888888888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ9111111111-1-1-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-111-1-1
χ10111111111-1-1-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1-111-1-111
χ11111111111-1-1-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11-1-11111-1-1
χ12111111111-1-1-1-111-1-1-1-11111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-111-1-1-1-111
χ13111111111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-11-1-1-111-1-111
χ14111111111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-11-1111-1-111-1-1
χ15111111111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1111-1-1-1-111
χ16111111111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-11111-1-1
χ171111-1-1-1-1-111-1-1-1111-1-111-1-111-111-1-1ii−i−iii−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-111-1-1i−ii−ii−ii−i
χ181111-1-1-1-1-111-1-1-1111-1-111-1-111-111-1-1ii−i−iii−i−iii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111-1-111−ii−ii−ii−ii
χ191111-1-1-1-1-111-1-1-1111-1-111-1-111-111-1-1ii−i−iii−i−iii−i−iii−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1-1-111−ii−iii−ii−i
χ201111-1-1-1-1-111-1-1-1111-1-111-1-111-111-1-1ii−i−iii−i−iii−i−iii−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-111-1-11111-1-1i−ii−i−ii−ii
χ211111-1-1-1-1-111-1-1-1111-1-111-1-111-111-1-1−i−iii−i−iii−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-111-1-1−ii−ii−ii−ii
χ221111-1-1-1-1-111-1-1-1111-1-111-1-111-111-1-1−i−iii−i−iii−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111-1-111i−ii−ii−ii−i
χ231111-1-1-1-1-111-1-1-1111-1-111-1-111-111-1-1−i−iii−i−iii−i−iii−i−iii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1-1-111i−ii−i−ii−ii
χ241111-1-1-1-1-111-1-1-1111-1-111-1-111-111-1-1−i−iii−i−iii−i−iii−i−iii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-111-1-11111-1-1−ii−iii−ii−i
χ251111-1-1-1-1-1-1-111-11-1-11111-1-111-1-1-111ii−i−i−i−iiiii−i−i−i−iii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-1111-1-11i−i−iii−i−ii
χ261111-1-1-1-1-1-1-111-11-1-11111-1-111-1-1-111ii−i−i−i−iiiii−i−i−i−iii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1-111-1−iii−i−iii−i
χ271111-1-1-1-1-1-1-111-11-1-11111-1-111-1-1-111ii−i−i−i−iiiii−i−i−i−iii-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111-111-1−iii−ii−i−ii
χ281111-1-1-1-1-1-1-111-11-1-11111-1-111-1-1-111ii−i−i−i−iiiii−i−i−i−iii-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-11-1-11i−i−ii−iii−i
χ291111-1-1-1-1-1-1-111-11-1-11111-1-111-1-1-111−i−iiiii−i−i−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-1111-1-11−iii−i−iii−i
χ301111-1-1-1-1-1-1-111-11-1-11111-1-111-1-1-111−i−iiiii−i−i−i−iiiii−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1-111-1i−i−iii−i−ii
χ311111-1-1-1-1-1-1-111-11-1-11111-1-111-1-1-111−i−iiiii−i−i−i−iiiii−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111-111-1i−i−ii−iii−i
χ321111-1-1-1-1-1-1-111-11-1-11111-1-111-1-1-111−i−iiiii−i−i−i−iiiii−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-11-1-11−iii−ii−i−ii
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χ342222222222222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000000000000000
χ35222222222-2-2-2-222-2-2-2-2-2-2-2-22-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000000000000000
χ36222222222-2-2-2-222-2-2-2-2-2-2-2-22-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000000000000000
χ3722222222-222-2-2-2-2-2-2222222-2-2-22-22-20000000000000000000000000000000022-2-222-2-222-2-222-2-200000000000000000000
χ3822222222-222-2-2-2-2-2-2222222-2-2-22-22-200000000000000000000000000000000-2-222-2-222-2-222-2-22200000000000000000000
χ3922222222-222-2-2-2-2-2-222-2-2-2-2-222-22-2200000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ4022222222-222-2-2-2-2-2-222-2-2-2-2-222-22-220000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ4122222222-2-2-222-2-222-2-22222-2-2-2-22-220000000000000000000000000000000022-2-222-2-2-2-222-2-22200000000000000000000
χ4222222222-2-2-222-2-222-2-22222-2-2-2-22-2200000000000000000000000000000000-2-222-2-22222-2-222-2-200000000000000000000
χ4322222222-2-2-222-2-222-2-2-2-2-2-2-2222-22-200000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
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χ452222-2-2-2-2222222-2-2-2-2-222-2-2-2-222-2-22000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000
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χ472222-2-2-2-2222222-2-2-2-2-2-2-222-22-2-222-200000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ482222-2-2-2-2222222-2-2-2-2-2-2-222-22-2-222-20000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
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χ502222-2-2-2-22-2-2-2-22-2222222-2-2-2-22-222-200000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000
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χ562222-2-2-2-2-2-2-222-22-2-222-2-2222-2222-2-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000
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χ832-2-22-2-222-22-2-222-22-2-220000200000000000000-222-2-222-22−22−2−22−222−22−2−22−22−22−222−22−2−22−222−22−200000000000000000000
χ842-2-22-2-222-22-2-222-22-2-220000200000000000000-222-2-222-2−22−222−22−2−22−222−22−22−22−2−22−222−22−2−22−2200000000000000000000
χ852-2-22-2-222-2-222-22-2-222-200002000000000000002-2-22-222-22−22−2−22−22−22−222−22−22−22−2−22−22−22−222−22−200000000000000000000
χ862-2-22-2-222-2-222-22-2-222-200002000000000000002-2-22-222-2−22−222−22−22−22−2−22−22−22−222−22−22−22−2−22−2200000000000000000000
χ872-2-22-2-222-2-222-22-2-222-20000200000000000000-222-22-2-222−22−2−22−22−22−222−22−2−22−222−22−22−22−2−22−2200000000000000000000
χ882-2-22-2-222-2-222-22-2-222-20000200000000000000-222-22-2-22−22−222−22−22−22−2−22−222−22−2−22−22−22−222−22−200000000000000000000
χ8944-4-44i−4i4i−4i000000000004-44i−4i0000000000000000000000000000000000000000000000000000000000022−222i2−2i2000000000000
χ9044-4-44i−4i4i−4i000000000004-44i−4i00000000000000000000000000000000000000000000000000000000000−2222−2i22i2000000000000
χ9144-4-44i−4i4i−4i00000000000-44−4i4i00000000000000000000000000000000000000000000000000000002i2−2i222−220000000000000000
χ9244-4-44i−4i4i−4i00000000000-44−4i4i0000000000000000000000000000000000000000000000000000000−2i22i2−22220000000000000000
χ9344-4-4−4i4i−4i4i000000000004-4−4i4i0000000000000000000000000000000000000000000000000000000000022−22−2i22i2000000000000
χ9444-4-4−4i4i−4i4i000000000004-4−4i4i00000000000000000000000000000000000000000000000000000000000−22222i2−2i2000000000000
χ9544-4-4−4i4i−4i4i00000000000-444i−4i00000000000000000000000000000000000000000000000000000002i2−2i2−22220000000000000000
χ9644-4-4−4i4i−4i4i00000000000-444i−4i0000000000000000000000000000000000000000000000000000000−2i22i222−220000000000000000
χ978-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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