Finite Group Databasebeta

← Group #202858

Character table — Group #202858

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222244444444444444444444444444444444444444444444444444444488888888161616161616161616161616
order12222222222244444444444444444444444444444444448888888888888888888888888888888888888888444444448888
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
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ911111111-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ1111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-111-1-1
χ1311111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-11111-1-1
χ1411111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-111
χ1511111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ1611111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ1711-1-1-111-111-1-11-111-1-11-1-11-11iiii−i−i−i−iii−i−i1-111-1-1ii−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
χ1811-1-1-111-111-1-11-111-1-11-1-11-11iiii−i−i−i−iii−i−i1-111-1-1ii−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
χ1911-1-1-111-111-1-11-111-1-11-1-11-11iiii−i−i−i−iii−i−i1-111-1-1ii−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
χ2011-1-1-111-111-1-11-111-1-11-1-11-11iiii−i−i−i−iii−i−i1-111-1-1ii−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
χ2111-1-1-111-111-1-11-111-1-11-1-11-11−i−i−i−iiiii−i−iii1-111-1-1−i−iiiiiii−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
χ2211-1-1-111-111-1-11-111-1-11-1-11-11−i−i−i−iiiii−i−iii1-111-1-1−i−iiiiiii−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
χ2311-1-1-111-111-1-11-111-1-11-1-11-11−i−i−i−iiiii−i−iii1-111-1-1−i−iii−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
χ2411-1-1-111-111-1-11-111-1-11-1-11-11−i−i−i−iiiii−i−iii1-111-1-1−i−iii−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
χ2511-1-1-111-1-1-1111-1-1-1111-1-11-11iiii−i−i−i−i−i−iii1-1-1-111−i−iiiiiii−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
χ2611-1-1-111-1-1-1111-1-1-1111-1-11-11iiii−i−i−i−i−i−iii1-1-1-111−i−iiiiiii−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
χ2711-1-1-111-1-1-1111-1-1-1111-1-11-11iiii−i−i−i−i−i−iii1-1-1-111−i−iii−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
χ2811-1-1-111-1-1-1111-1-1-1111-1-11-11iiii−i−i−i−i−i−iii1-1-1-111−i−iii−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
χ2911-1-1-111-1-1-1111-1-1-1111-1-11-11−i−i−i−iiiiiii−i−i1-1-1-111ii−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
χ3011-1-1-111-1-1-1111-1-1-1111-1-11-11−i−i−i−iiiiiii−i−i1-1-1-111ii−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
χ3111-1-1-111-1-1-1111-1-1-1111-1-11-11−i−i−i−iiiiiii−i−i1-1-1-111ii−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
χ3211-1-1-111-1-1-1111-1-1-1111-1-11-11−i−i−i−iiiiiii−i−i1-1-1-111ii−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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χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000022-22-2200000000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ3922222222-2-2-2-222-2-2-2-2-2-2-222-222-2-222-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-222-2-2-2-2-2-2-222-2-2-222-2-2222222-2-22222-2-2-2-20000000000000000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-22222222-2-22000000000000-2-2-22-22000022-2-222-2-2-2-222-2-222000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-22222222-2-22000000000000-2-2-22-220000-2-222-2-22222-2-222-2-2000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-22222-2-2-2-2-2-2000000000000222-22-2000000000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000
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χ452222-2-2-2-22-22-2222-22-2000-2-202-2002-2002-22-200000000002−22−22−22−22−22−22−22−22−22−22−22−22−22−22−22−200000000000000000000
χ462222-2-2-2-22-22-2222-22-2000-2-202-2002-2002-22-20000000000−22−22−22−22−22−22−22−22−22−22−22−22−22−22−22−2200000000000000000000
χ472222-2-2-2-22-22-2222-22-2000-2-20-2200-2200-22-2200000000002−22−22−22−22−22−22−22−2−22−22−22−22−22−22−22−2200000000000000000000
χ482222-2-2-2-22-22-2222-22-2000-2-20-2200-2200-22-220000000000−22−22−22−22−22−22−22−222−22−22−22−22−22−22−22−200000000000000000000
χ492222-2-2-2-22-22-2-2-2-22-22000220002i−2i002i−2i00000000002i−2i2i−2i2−2−222−2−222−2−222−2−22i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000000000000000
χ502222-2-2-2-22-22-2-2-2-22-22000220002i−2i002i−2i00000000002i−2i2i−2i−222−2−222−2−222−2−222−2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000000000000000
χ512222-2-2-2-22-22-2-2-2-22-2200022000−2i2i00−2i2i0000000000−2i2i−2i2i2−2−222−2−222−2−222−2−22−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000000000000000
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χ532222-2-2-2-2-22-2222-22-22000-2-202-2002-200-22-2200000000002−22−22−22−2−22−22−22−222−22−22−22−2−22−22−22−2200000000000000000000
χ542222-2-2-2-2-22-2222-22-22000-2-202-2002-200-22-220000000000−22−22−22−222−22−22−22−2−22−22−22−222−22−22−22−200000000000000000000
χ552222-2-2-2-2-22-2222-22-22000-2-20-2200-22002-22-200000000002−22−22−22−2−22−22−22−22−22−22−22−222−22−22−22−200000000000000000000
χ562222-2-2-2-2-22-2222-22-22000-2-20-2200-22002-22-20000000000−22−22−22−222−22−22−22−22−22−22−22−2−22−22−22−2200000000000000000000
χ572222-2-2-2-2-22-22-2-22-22-2000220002i−2i002i−2i0000000000−2i2i−2i2i2−2−222−2−22−222−2−222−2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000000000000000
χ582222-2-2-2-2-22-22-2-22-22-2000220002i−2i002i−2i0000000000−2i2i−2i2i−222−2−222−22−2−222−2−22−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000000000000000
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χ7422-2-22-2-22-222-2-222-2-220002-20002-200-220000000000-222-2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000000000000000
χ7522-2-22-2-22-222-2-222-2-220002-2000-22002-200000000002-2-22i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000000000000000
χ7622-2-22-2-22-222-2-222-2-220002-2000-22002-200000000002-2-22−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000000000000000
χ7722-2-2-222-222-2-22-222-2-2-2222-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i-22-2-222−2i−2i2i2i0000000000000000000000000000000000000000000000000000
χ7822-2-2-222-222-2-22-222-2-2-2222-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i-22-2-2222i2i−2i−2i0000000000000000000000000000000000000000000000000000
χ7922-2-2-222-222-2-2-22-2-2222-2-2-222000000000000-222-2-2200002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
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χ8222-2-2-222-222-2-2-22-2-222-222-22-20000000000002-2-222-200000000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ8322-2-2-222-2-2-2222-2-2-222-2222-2-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i-2222-2-22i2i−2i−2i0000000000000000000000000000000000000000000000000000
χ8422-2-2-222-2-2-2222-2-2-222-2222-2-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i-2222-2-2−2i−2i2i2i0000000000000000000000000000000000000000000000000000
χ8522-2-2-222-2-2-222-2222-2-22-2-2-222000000000000-22-222-200002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ8622-2-2-222-2-2-222-2222-2-22-2-2-222000000000000-22-222-20000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ8722-2-2-222-2-2-222-2222-2-2-222-22-20000000000002-22-2-22000000000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ8822-2-2-222-2-2-222-2222-2-2-222-22-20000000000002-22-2-2200000000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000
χ894-44-444-4-4000000000044-400-4000000000000000000000000000000000000000000000000000000000022−2222−22000000000000
χ904-44-444-4-4000000000044-400-40000000000000000000000000000000000000000000000000000000000−2222−2222000000000000
χ914-44-444-4-40000000000-4-440040000000000000000000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ924-44-444-4-40000000000-4-44004000000000000000000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ934-4-44-44-4400000000004-4400-400000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ944-4-44-44-4400000000004-4400-40000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ954-4-44-44-440000000000-44-400400000000000000000000000000000000000000000000000000000022−22−22220000000000000000
χ964-4-44-44-440000000000-44-4004000000000000000000000000000000000000000000000000000000−222222−220000000000000000
χ978-88-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-8-888-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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