Finite Group Databasebeta

← Group #189136

Character table — Group #189136

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
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-111111-1-1-1-1111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111-1-1-1-111111-1-1-1-1111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ1111111111-1-1-1-111111-1-1-1-1111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111-1-111
χ1211111111-1-1-1-111111-1-1-1-1111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-111-1-1
χ1311111111-1-1-1-111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-111
χ1411111111-1-1-1-111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-11111-1-1
χ1511111111-1-1-1-111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ1611111111-1-1-1-111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ171-1-11-111-111-1-1-1-111-111-1-111-11-11-11-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−ii−ii−ii−ii−ii−ii−i
χ181-1-11-111-111-1-1-1-111-111-1-111-11-11-11-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−ii−ii−ii−ii−ii−ii
χ191-1-11-111-111-1-1-1-111-111-1-111-11-11-11-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−iii−ii−i−ii−ii−ii
χ201-1-11-111-111-1-1-1-111-111-1-111-11-11-11-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111−i−iii−i−iiii−i−ii−iii−ii−ii−i
χ211-1-11-111-111-1-1-1-111-111-1-111-11-11-11-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−ii−i−ii−iii−i−ii−ii
χ221-1-11-111-111-1-1-1-111-111-1-111-11-11-11-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iii−iii−ii−i−iii−ii−i
χ231-1-11-111-111-1-1-1-111-111-1-111-11-11-11-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1ii−i−iii−i−i−ii−ii−ii−iii−ii−i
χ241-1-11-111-111-1-1-1-111-111-1-111-11-11-11-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1−i−iii−i−iiii−ii−ii−ii−i−ii−ii
χ251-1-11-111-1-1-111-1-111-1-1-11111-1-111-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiii−ii−i−ii−iii−i−ii
χ261-1-11-111-1-1-111-1-111-1-1-11111-1-111-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−ii−iii−ii−i−iii−i
χ271-1-11-111-1-1-111-1-111-1-1-11111-1-111-1-111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−iii−i−iii−i−iii−i
χ281-1-11-111-1-1-111-1-111-1-1-11111-1-111-1-111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−ii−i−iii−i−iii−i−ii
χ291-1-11-111-1-1-111-1-111-1-1-11111-1-111-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1ii−i−i−i−iiii−i−iii−i−ii−iii−i
χ301-1-11-111-1-1-111-1-111-1-1-11111-1-111-1-11-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−iii−i−iii−ii−i−ii
χ311-1-11-111-1-1-111-1-111-1-1-11111-1-111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iii−ii−iii−ii−ii−i−ii
χ321-1-11-111-1-1-111-1-111-1-1-11111-1-111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−ii−ii−i−ii−ii−iii−i
χ3322222222222222-2-2-2-2-2-2-222-222-2-2-2-20000000000000000000000000000000022-2-222-2-222-2-222-2-200000000000000000000
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χ38222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
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χ4022222222-2-2-2-222-2-2-2222222-2-2-2-2-22200000000000000000000000000000000-2-222-2-22222-2-222-2-200000000000000000000
χ4122222222-2-2-2-2-2-2222-2-2-2-2-2-2222-2-22222-2-222-2-2-2-222-2-2220000000000000000000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-2222-2-2-2-2-2-2222-2-222-2-222-2-22222-2-222-2-20000000000000000000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-22222-2-2-22222-2-200000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-22222-2-2-22222-2-20000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ45222-2-22-2-22-22-2002-222-22-200-2000000002-2002-2002-2002-22−22−22−22−22−22−22−22−22−22−22−22−22−22−22−22−200000000000000000000
χ46222-2-22-2-22-22-2002-222-22-200-2000000002-2002-2002-2002-2−22−22−22−22−22−22−22−22−22−22−22−22−22−22−22−2200000000000000000000
χ47222-2-22-2-22-22-2002-222-22-200-200000000-2200-2200-2200-222−22−22−22−22−22−22−22−2−22−22−22−22−22−22−22−2200000000000000000000
χ48222-2-22-2-22-22-2002-222-22-200-200000000-2200-2200-2200-22−22−22−22−22−22−22−22−222−22−22−22−22−22−22−22−200000000000000000000
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χ50222-2-22-2-22-22-200-22-2-22-220020000002i−2i002i−2i002i−2i002i−2i00−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−222−2−222−2−222−2−222−200000000000000000000
χ51222-2-22-2-22-22-200-22-2-22-22002000000−2i2i00−2i2i00−2i2i00−2i2i00i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2−222−2−222−2−222−2−222−200000000000000000000
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χ53222-2-22-2-2-22-22002-22-22-2200-2000000002-2002-200-2200-222−22−22−22−2−22−22−22−222−22−22−22−2−22−22−22−2200000000000000000000
χ54222-2-22-2-2-22-22002-22-22-2200-2000000002-2002-200-2200-22−22−22−22−222−22−22−22−2−22−22−22−222−22−22−22−200000000000000000000
χ55222-2-22-2-2-22-22002-22-22-2200-200000000-2200-22002-2002-22−22−22−22−2−22−22−22−22−22−22−22−222−22−22−22−200000000000000000000
χ56222-2-22-2-2-22-22002-22-22-2200-200000000-2200-22002-2002-2−22−22−22−222−22−22−22−22−22−22−22−2−22−22−22−2200000000000000000000
χ57222-2-22-2-2-22-2200-22-22-22-20020000002i−2i002i−2i00−2i2i00−2i2i00i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i22−2−222−2−22−222−2−222−200000000000000000000
χ58222-2-22-2-2-22-2200-22-22-22-20020000002i−2i002i−2i00−2i2i00−2i2i00−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−222−2−222−22−2−222−2−2200000000000000000000
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χ822-2-2-222-22-222-2002-2-2-222-2002000000002-200-2200-22002-2−22−222−22−22−22−2−22−22−22−222−22−22−22−2−22−2200000000000000000000
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χ964-444-4-4-440000-4400000004-40000000000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ9788-8-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-88-88-88-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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