Finite Group Databasebeta

← Group #202861

Character table — Group #202861

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222244444444444444444444444444444444444444444444444444444488888888161616161616161616161616
order12222222444444444444444422444444444444444444448888888888888888888888888888888888888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ9111111111-1-1-1-1-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ10111111111-1-1-1-1-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ11111111111-1-1-1-1-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-111
χ12111111111-1-1-1-1-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-111-1-1
χ13111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-11111-1-1
χ14111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-111
χ15111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ16111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ17111-1-11-1-1111-1-111-1-111-1-1-1-111-11-1iiii−i−i−i−i1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i1-11-1i−ii−i1-11-1
χ18111-1-11-1-1111-1-111-1-111-1-1-1-111-11-1iiii−i−i−i−i1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1−i−iii−i−iii-11-11−ii−ii-11-11
χ19111-1-11-1-1111-1-111-1-111-1-1-1-111-11-1iiii−i−i−i−i1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111ii−i−iii−i−i1-11-1−ii−ii-11-11
χ20111-1-11-1-1111-1-111-1-111-1-1-1-111-11-1iiii−i−i−i−i1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111−i−iii−i−iii-11-11i−ii−i1-11-1
χ21111-1-11-1-1111-1-111-1-111-1-1-1-111-11-1−i−i−i−iiiii1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111ii−i−iii−i−i-11-11−ii−ii1-11-1
χ22111-1-11-1-1111-1-111-1-111-1-1-1-111-11-1−i−i−i−iiiii1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−iii−i−iii1-11-1i−ii−i-11-11
χ23111-1-11-1-1111-1-111-1-111-1-1-1-111-11-1−i−i−i−iiiii1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i-11-11i−ii−i-11-11
χ24111-1-11-1-1111-1-111-1-111-1-1-1-111-11-1−i−i−i−iiiii1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii1-11-1−ii−ii1-11-1
χ25111-1-11-1-11-1-111-1-11111-1-1-1-11-11-11iiii−i−i−i−i1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ii−i−i−i−iii1-1-11i−i−ii1-1-11
χ26111-1-11-1-11-1-111-1-11111-1-1-1-11-11-11iiii−i−i−i−i1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−i−iiiii−i−i-111-1−iii−i-111-1
χ27111-1-11-1-11-1-111-1-11111-1-1-1-11-11-11iiii−i−i−i−i1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1ii−i−i−i−iii1-1-11−iii−i-111-1
χ28111-1-11-1-11-1-111-1-11111-1-1-1-11-11-11iiii−i−i−i−i1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1−i−iiiii−i−i-111-1i−i−ii1-1-11
χ29111-1-11-1-11-1-111-1-11111-1-1-1-11-11-11−i−i−i−iiiii1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1ii−i−i−i−iii-111-1−iii−i1-1-11
χ30111-1-11-1-11-1-111-1-11111-1-1-1-11-11-11−i−i−i−iiiii1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−iiiii−i−i1-1-11i−i−ii-111-1
χ31111-1-11-1-11-1-111-1-11111-1-1-1-11-11-11−i−i−i−iiiii1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111ii−i−i−i−iii-111-1i−i−ii-111-1
χ32111-1-11-1-11-1-111-1-11111-1-1-1-11-11-11−i−i−i−iiiii1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−iiiii−i−i1-1-11−iii−i1-1-11
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χ342222222222222-2-2-2-2-2-222-2-2222-2-200000000-2-200000000-2-222-2-222-2-222-2-222000000000000000000000000000000000000
χ35222222222-2-2-2-22222-2-222-2-22-2-22200000000-2-20000000022-2-222-2-2-2-222-2-222000000000000000000000000000000000000
χ36222222222-2-2-2-22222-2-222-2-22-2-22200000000-2-200000000-2-222-2-22222-2-222-2-2000000000000000000000000000000000000
χ3722222222-22222222222-2-222-2-2-2-2-222-2-222-2-2-2-222-2-222-2-20000000000000000000000000000000000000000000000000000
χ3822222222-22222222222-2-222-2-2-2-2-2-2-222-2-222-2-2-2-222-2-2220000000000000000000000000000000000000000000000000000
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χ4222222222-2-2-2-2-22222-2-2-2-2-2-2-222-2-20000000022000000000000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-222-2-222-2222222-2-222-2-2-2-2-2-222-2-2220000000000000000000000000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-222-2-222-22222-2-222-2-222-2-222-2-222-2-20000000000000000000000000000000000000000000000000000
χ45222-2-22-2-2222-2-2-2-222-2-2-2-22222-2-2200000000-22000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ46222-2-22-2-2222-2-2-2-222-2-2-2-22222-2-2200000000-2200000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
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χ48222-2-22-2-22-2-22222-2-2-2-2-2-2222-222-200000000-2200000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ49222-2-22-2-2-222-2-222-2-22222-2-2-2-22-222i2i−2i−2i−2i−2i2i2i-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000
χ50222-2-22-2-2-222-2-222-2-22222-2-2-2-22-22−2i−2i2i2i2i2i−2i−2i-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000
χ51222-2-22-2-2-222-2-2-2-222-2-22222-2-222-2000000002-20000000000000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000
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χ55222-2-22-2-2-2-2-222-2-2222222-2-2-22-22-22i2i−2i−2i−2i−2i2i2i-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000
χ56222-2-22-2-2-2-2-222-2-2222222-2-2-22-22-2−2i−2i2i2i2i2i−2i−2i-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000
χ5722-22-2-22-202i−2i2i−2i2i−2i2i−2i2-2002-200000002i−2i002i−2i00002-2002-2i2−i2i2−i2i2−i2i2−i22−22−22−22−22−22−22−22−2i2−i2i2−i2i2−i2i2−i200000000000000000000
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χ7222-22-2-22-20−2i2i−2i2i−2i2i−2i2i2-2002-20000000−2i2i00−2i2i00002-2002-2−i2i2−i2i2−i2i2−i2i22−22−22−22−22−22−22−22−2−i2i2−i2i2−i2i2−i2i200000000000000000000
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χ7522-2-22-2-2202i−2i−2i2i2i−2i−2i2i2-200-220000000-22002-200002i−2i00−2i2i2−22−2−22−22−i2i2−i2i2i2−i2i2−i2−22−222−22−2−i2i2−i2i2i2−i2i2−i200000000000000000000
χ7622-2-22-2-2202i−2i−2i2i2i−2i−2i2i2-200-220000000-22002-200002i−2i00−2i2i−22−222−22−2i2−i2i2−i2−i2i2−i2i22−22−2−22−22i2−i2i2−i2−i2i2−i2i200000000000000000000
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χ8022-2-22-2-2202i−2i−2i2i−2i2i2i−2i-22002-200000−2i2i002i−2i00002-200-2200−222−22−2−22i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i22−2−22−222−200000000000000000000
χ8122-2-22-2-220−2i2i2i−2i2i−2i−2i2i-22002-2000002i−2i00−2i2i00002-200-22002−2−22−222−2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−222−22−2−2200000000000000000000
χ8222-2-22-2-220−2i2i2i−2i2i−2i−2i2i-22002-2000002i−2i00−2i2i00002-200-2200−222−22−2−22−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i22−2−22−222−200000000000000000000
χ8322-2-22-2-220−2i2i2i−2i2i−2i−2i2i-22002-200000−2i2i002i−2i0000-22002-2002−2−22−222−2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i22−2−22−222−200000000000000000000
χ8422-2-22-2-220−2i2i2i−2i2i−2i−2i2i-22002-200000−2i2i002i−2i0000-22002-200−222−22−2−22−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−222−22−2−2200000000000000000000
χ8522-2-22-2-220−2i2i2i−2i−2i2i2i−2i2-200-2200000002-200-2200002i−2i00−2i2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i22−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000000000000000
χ8622-2-22-2-220−2i2i2i−2i−2i2i2i−2i2-200-2200000002-200-2200002i−2i00−2i2i−22−222−22−2−i2i2−i2i2i2−i2i2−i2−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000000000000000
χ8722-2-22-2-220−2i2i2i−2i−2i2i2i−2i2-200-220000000-22002-20000−2i2i002i−2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i2−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000000000000000
χ8822-2-22-2-220−2i2i2i−2i−2i2i2i−2i2-200-220000000-22002-20000−2i2i002i−2i−22−222−22−2−i2i2−i2i2i2−i2i2−i22−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000000000000000
χ894-4444-4-4-4400000000004-400-400000000000000000000000000000000000000000000000000000022−2222−220000000000000000
χ904-4444-4-4-4400000000004-400-4000000000000000000000000000000000000000000000000000000−2222−22220000000000000000
χ914-4444-4-4-4-40000000000-4400400000000000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ924-4444-4-4-4-40000000000-440040000000000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ934-44-4-4-44440000000000-4400-40000000000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ944-44-4-4-44440000000000-4400-4000000000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ954-44-4-4-444-400000000004-4004000000000000000000000000000000000000000000000000000000000022−22−2222000000000000
χ964-44-4-4-444-400000000004-40040000000000000000000000000000000000000000000000000000000000−222222−22000000000000
χ978-8-88-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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