Finite Group Databasebeta

← Group #211294

Character table — Group #211294

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222244444444444444444444444444444444444444444444444444444488888888161616161616161616161616
order12222222444444444444444422224444444444444444448888888888888888888888888888888888888888444444448888
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
χ5111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ911111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-11111-1-1
χ1411111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-111
χ1511111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ1611111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
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χ191-11-111-1-1ii−i−iii−i−i1-111-1-11-111-1-1i−i11-1-1ii−i−i1-1i−iii−i−i-1-111−i−iii-1-111−i−iii-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i1-1i−i-11−ii-11−ii
χ201-11-111-1-1ii−i−iii−i−i1-111-1-11-111-1-1i−i11-1-1ii−i−i1-1i−iii−i−i-1-111−i−iii-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-1-111−i−iii-11−ii1-1i−i1-1i−i
χ211-11-111-1-1ii−i−iii−i−i1-111-1-11-1-1-111i−i-1-111−i−iii1-1i−i−i−iii11-1-1ii−i−i11-1-1ii−i−i-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i-11−ii-11−ii1-1i−i
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χ231-11-111-1-1ii−i−iii−i−i1-111-1-11-1-1-111i−i-1-111−i−iii1-1i−i−i−iii-1-111−i−iii-1-111−i−iii1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i-11−ii1-1i−i-11−ii
χ241-11-111-1-1ii−i−iii−i−i1-111-1-11-1-1-111i−i-1-111−i−iii1-1i−i−i−iii-1-111−i−iii-1-111−i−iii1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii1-1i−i-11−ii1-1i−i
χ251-11-111-1-1−i−iii−i−iii1-111-1-11-111-1-1−ii11-1-1−i−iii1-1−ii−i−iii11-1-1−i−iii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii1-1−ii1-1−ii1-1−ii
χ261-11-111-1-1−i−iii−i−iii1-111-1-11-111-1-1−ii11-1-1−i−iii1-1−ii−i−iii11-1-1−i−iii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i-11i−i-11i−i-11i−i
χ271-11-111-1-1−i−iii−i−iii1-111-1-11-111-1-1−ii11-1-1−i−iii1-1−ii−i−iii-1-111ii−i−i-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii1-1−ii-11i−i-11i−i
χ281-11-111-1-1−i−iii−i−iii1-111-1-11-111-1-1−ii11-1-1−i−iii1-1−ii−i−iii-1-111ii−i−i-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i-11i−i1-1−ii1-1−ii
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χ301-11-111-1-1−i−iii−i−iii1-111-1-11-1-1-111−ii-1-111ii−i−i1-1−iiii−i−i11-1-1−i−iii11-1-1−i−iii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i1-1−ii1-1−ii-11i−i
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χ321-11-111-1-1−i−iii−i−iii1-111-1-11-1-1-111−ii-1-111ii−i−i1-1−iiii−i−i-1-111ii−i−i-1-111ii−i−i1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i1-1−ii-11i−i1-1−ii
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χ802-2-222-22-22-2-22-222-200-222-200-222-2000000-222-200000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000000000000000
χ812-2-222-22-2-222-22-2-2200-222-2002-2-22000000-222-200000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000000000000000
χ822-2-222-22-2-222-22-2-2200-222-2002-2-22000000-222-200000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000000000000000
χ832-2-222-22-2-222-22-2-2200-222-200-222-20000002-2-2200000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000000000000000
χ842-2-222-22-2-222-22-2-2200-222-200-222-20000002-2-2200000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000000000000000
χ852-2-222-22-2-222-2-222-2002-2-22000000002i−2i−2i2i000000002i−2i−2i2ii2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i22−22−2−22−22−22−222−22−200000000000000000000
χ862-2-222-22-2-222-2-222-2002-2-22000000002i−2i−2i2i000000002i−2i−2i2i−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−22−222−22−22−22−2−22−2200000000000000000000
χ872-2-222-22-2-222-2-222-2002-2-2200000000−2i2i2i−2i00000000−2i2i2i−2ii2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−22−222−22−22−22−2−22−2200000000000000000000
χ882-2-222-22-2-222-2-222-2002-2-2200000000−2i2i2i−2i00000000−2i2i2i−2i−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i22−22−2−22−22−22−222−22−200000000000000000000
χ89444-4-4-44-400000000440000-4-4000000000000000000000000000000000000000000000000000000000022−2222−22000000000000
χ90444-4-4-44-400000000440000-4-40000000000000000000000000000000000000000000000000000000000−2222−2222000000000000
χ91444-4-4-44-400000000-4-40000440000000000000000000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ92444-4-4-44-400000000-4-4000044000000000000000000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ934-444-4-4-44000000004-40000-4400000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ944-444-4-4-44000000004-40000-440000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ954-444-4-4-4400000000-4400004-40000000000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ964-444-4-4-4400000000-4400004-4000000000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ9788-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-8-8-8-8888000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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