Finite Group Databasebeta

← Group #211288

Character table — Group #211288

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222244444444444444444444444444444444444444444444444444444488888888161616161616161616161616
order12222222444444444444444444444444444444444444448888888888888888888888888888888888888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-111-1-111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111
χ911111111-1-1-1-111-1-1-1-1111111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111-1-1-1-111-1-1-1-1111111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ1111111111-1-1-1-111-1-1-1-1111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-111-1-1-1-1111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-111-1-1
χ1311111111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1
χ1411111111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-111
χ1511111111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ1611111111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ1711-11-1-11-1ii−i−i1-1ii−i−i1-11-11-1i−i1-1i−iiiii−i−i−i−i11-1-111-1-111-1-1ii−i−i11-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−i11-1-11-11-1i−ii−ii−i1-1
χ1811-11-1-11-1ii−i−i1-1ii−i−i1-11-11-1i−i1-1i−iiiii−i−i−i−i11-1-111-1-111-1-1ii−i−i11-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1−i−iii-1-111-11-11−ii−ii−ii-11
χ1911-11-1-11-1ii−i−i1-1ii−i−i1-11-11-1i−i1-1i−iiiii−i−i−i−i11-1-111-1-1-1-111−i−iii-1-111−i−iii−i−i−i−iiiii-1-1-1-11111ii−i−i11-1-11-1-11i−i−ii−ii-11
χ2011-11-1-11-1ii−i−i1-1ii−i−i1-11-11-1i−i1-1i−iiiii−i−i−i−i11-1-111-1-1-1-111−i−iii-1-111−i−iii−i−i−i−iiiii-1-1-1-11111−i−iii-1-111-111-1−iii−ii−i1-1
χ2111-11-1-11-1ii−i−i1-1ii−i−i1-11-11-1i−i1-1i−i−i−i−i−iiiii-1-111-1-11111-1-1ii−i−i11-1-1ii−i−i−i−i−i−iiiii-1-1-1-11111ii−i−i11-1-1-11-11−ii−iii−i1-1
χ2211-11-1-11-1ii−i−i1-1ii−i−i1-11-11-1i−i1-1i−i−i−i−i−iiiii-1-111-1-11111-1-1ii−i−i11-1-1ii−i−i−i−i−i−iiiii-1-1-1-11111−i−iii-1-1111-11-1i−ii−i−ii-11
χ2311-11-1-11-1ii−i−i1-1ii−i−i1-11-11-1i−i1-1i−i−i−i−i−iiiii-1-111-1-111-1-111−i−iii-1-111−i−iiiiiii−i−i−i−i1111-1-1-1-1ii−i−i11-1-1-111-1−iii−i−ii-11
χ2411-11-1-11-1ii−i−i1-1ii−i−i1-11-11-1i−i1-1i−i−i−i−i−iiiii-1-111-1-111-1-111−i−iii-1-111−i−iiiiiii−i−i−i−i1111-1-1-1-1−i−iii-1-1111-1-11i−i−iii−i1-1
χ2511-11-1-11-1−i−iii1-1−i−iii1-11-11-1−ii1-1−iiiiii−i−i−i−i-1-111-1-11111-1-1−i−iii11-1-1−i−iiiiiii−i−i−i−i-1-1-1-11111ii−i−i-1-1111-11-1−ii−iii−i-11
χ2611-11-1-11-1−i−iii1-1−i−iii1-11-11-1−ii1-1−iiiiii−i−i−i−i-1-111-1-11111-1-1−i−iii11-1-1−i−iiiiiii−i−i−i−i-1-1-1-11111−i−iii11-1-1-11-11i−ii−i−ii1-1
χ2711-11-1-11-1−i−iii1-1−i−iii1-11-11-1−ii1-1−iiiiii−i−i−i−i-1-111-1-111-1-111ii−i−i-1-111ii−i−i−i−i−i−iiiii1111-1-1-1-1ii−i−i-1-1111-1-11−iii−i−ii1-1
χ2811-11-1-11-1−i−iii1-1−i−iii1-11-11-1−ii1-1−iiiiii−i−i−i−i-1-111-1-111-1-111ii−i−i-1-111ii−i−i−i−i−i−iiiii1111-1-1-1-1−i−iii11-1-1-111-1i−i−iii−i-11
χ2911-11-1-11-1−i−iii1-1−i−iii1-11-11-1−ii1-1−ii−i−i−i−iiiii11-1-111-1-111-1-1−i−iii11-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1ii−i−i-1-111-11-11i−ii−ii−i-11
χ3011-11-1-11-1−i−iii1-1−i−iii1-11-11-1−ii1-1−ii−i−i−i−iiiii11-1-111-1-111-1-1−i−iii11-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−iii11-1-11-11-1−ii−ii−ii1-1
χ3111-11-1-11-1−i−iii1-1−i−iii1-11-11-1−ii1-1−ii−i−i−i−iiiii11-1-111-1-1-1-111ii−i−i-1-111ii−i−iiiii−i−i−i−i-1-1-1-11111ii−i−i-1-111-111-1i−i−ii−ii1-1
χ3211-11-1-11-1−i−iii1-1−i−iii1-11-11-1−ii1-1−ii−i−i−i−iiiii11-1-111-1-1-1-111ii−i−i-1-111ii−i−iiiii−i−i−i−i-1-1-1-11111−i−iii11-1-11-1-11−iii−ii−i-11
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χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000
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χ4022222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-222-2-222-2-2222222-2-2-2-20000000000000000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-222222222-2-222-2-2-2-2000000000000000022222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000
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χ4822-22-2-22-22i2i−2i−2i-22−2i−2i2i2i2-22-2-22−2i2i-222i−2i0000000000000000-2-2222i2i−2i−2i22-2-2−2i−2i2i2i000000000000000000000000000000000000
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χ782-2-2-2-22222-2-22-2-2-222-2000022000000002-200-2200002-2-22−222−22−2−222−2−22−222−2−222−22−2−222−2−22−222−200000000000000000000
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χ812-2-2-2-2222-222-222-222-20000-2-20000002i−2i00−2i2i002i−2i−2i2i00002−2−22−222−22−2−22−222−2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000000000000000
χ822-2-2-2-2222-222-222-222-20000-2-20000002i−2i00−2i2i002i−2i−2i2i0000−222−22−2−22−222−22−2−22−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000000000000000
χ832-2-2-2-2222-222-222-222-20000-2-2000000−2i2i002i−2i00−2i2i2i−2i00002−2−22−222−22−2−22−222−2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000000000000000
χ842-2-2-2-2222-222-222-222-20000-2-2000000−2i2i002i−2i00−2i2i2i−2i0000−222−22−2−22−222−22−2−22i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000000000000000
χ852-2-2-2-2222-222-2-2-22-2-22000022000000002-200-220000-222-22−2−222−2−22−222−2−222−22−2−22−222−22−2−22−222−200000000000000000000
χ862-2-2-2-2222-222-2-2-22-2-22000022000000002-200-220000-222-2−222−2−222−22−2−222−2−22−222−22−2−22−222−22−2−2200000000000000000000
χ872-2-2-2-2222-222-2-2-22-2-2200002200000000-22002-200002-2-222−2−222−2−22−222−2−222−2−222−22−2−22−222−22−2−2200000000000000000000
χ882-2-2-2-2222-222-2-2-22-2-2200002200000000-22002-200002-2-22−222−2−222−22−2−222−2−222−2−22−222−22−2−22−222−200000000000000000000
χ89444-4-4-4-4400000000004-4-44000000000000000000000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ90444-4-4-4-4400000000004-4-4400000000000000000000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ91444-4-4-4-440000000000-444-40000000000000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ92444-4-4-4-440000000000-444-4000000000000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ9344-4-444-4-4000000000044-4-40000000000000000000000000000000000000000000000000000000022−22−22220000000000000000
χ9444-4-444-4-4000000000044-4-400000000000000000000000000000000000000000000000000000000−222222−220000000000000000
χ9544-4-444-4-40000000000-4-4440000000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ9644-4-444-4-40000000000-4-444000000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ978-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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