Finite Group Databasebeta

← Group #205365

Character table — Group #205365

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222244444444444444444444444444444444444444444444444444444488888888161616161616161616161616
order12222222444444444444444422444444444444444444448888888888888888888888888888888888888888222244448888
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ101111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-111
χ121111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-111-1-1
χ131111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111
χ141111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11111-1-1
χ151111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ161111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
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χ181-1-11-1-111111111-1-1-1-111-1-1-1-11-11-1iiii−i−i−i−iiiii−i−i−i−i1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1−i−iii−i−iii-11-11-11-11−ii−ii
χ191-1-11-1-111111111-1-1-1-111-1-1-1-11-11-1iiii−i−i−i−iiiii−i−i−i−i1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111ii−i−iii−i−i1-1-111-1-11−ii−ii
χ201-1-11-1-111111111-1-1-1-111-1-1-1-11-11-1iiii−i−i−i−iiiii−i−i−i−i1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111−i−iii−i−iii-111-1-111-1i−ii−i
χ211-1-11-1-111111111-1-1-1-111-1-1-1-11-11-1−i−i−i−iiiii−i−i−i−iiiii1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111ii−i−iii−i−i-111-1-111-1−ii−ii
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χ231-1-11-1-111111111-1-1-1-111-1-1-1-11-11-1−i−i−i−iiiii−i−i−i−iiiii1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i-11-11-11-11i−ii−i
χ241-1-11-1-111111111-1-1-1-111-1-1-1-11-11-1−i−i−i−iiiii−i−i−i−iiiii1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii1-11-11-11-1−ii−ii
χ251-1-11-1-11111-1-1-1-1111111-1-1-1-1-11-11iiii−i−i−i−i−i−i−i−iiiii1-1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ii−i−i−i−iii1-11-1-11-11i−i−ii
χ261-1-11-1-11111-1-1-1-1111111-1-1-1-1-11-11iiii−i−i−i−i−i−i−i−iiiii1-1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−i−iiiii−i−i-11-111-11-1−iii−i
χ271-1-11-1-11111-1-1-1-1111111-1-1-1-1-11-11iiii−i−i−i−i−i−i−i−iiiii1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1ii−i−i−i−iii1-1-11-111-1−iii−i
χ281-1-11-1-11111-1-1-1-1111111-1-1-1-1-11-11iiii−i−i−i−i−i−i−i−iiiii1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1−i−iiiii−i−i-111-11-1-11i−i−ii
χ291-1-11-1-11111-1-1-1-1111111-1-1-1-1-11-11−i−i−i−iiiiiiiii−i−i−i−i1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1ii−i−i−i−iii-111-11-1-11−iii−i
χ301-1-11-1-11111-1-1-1-1111111-1-1-1-1-11-11−i−i−i−iiiiiiiii−i−i−i−i1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−iiiii−i−i1-1-11-111-1i−i−ii
χ311-1-11-1-11111-1-1-1-1111111-1-1-1-1-11-11−i−i−i−iiiiiiiii−i−i−i−i1-1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111ii−i−i−i−iii-11-111-11-1i−i−ii
χ321-1-11-1-11111-1-1-1-1111111-1-1-1-1-11-11−i−i−i−iiiiiiiii−i−i−i−i1-1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−iiiii−i−i1-11-1-11-11−iii−i
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χ362222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-222-2-22222-2-222-2-2-2-20000000000000000000000000000000000000000000000000000
χ3722222222-2-222-2-222-2-22222-2-222-2-20000000000000000-2-2000000000000000022-2-222-2-222-2-222-2-200000000000000000000
χ3822222222-2-222-2-222-2-22222-2-222-2-20000000000000000-2-20000000000000000-2-222-2-222-2-222-2-22200000000000000000000
χ3922222222-2-222-2-222-2-2-2-2-2-2-2-2-2-2220000000000000000222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
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χ4122222222-2-2-2-222-2-2222222-2-2-2-2220000000000000000-2-2000000000000000022-2-222-2-2-2-222-2-22200000000000000000000
χ4222222222-2-2-2-222-2-2222222-2-2-2-2220000000000000000-2-20000000000000000-2-222-2-22222-2-222-2-200000000000000000000
χ4322222222-2-2-2-222-2-222-2-2-2-2-2-222-2-20000000000000000222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
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χ772-2-22-2-222222222-2-2-2-2-2-222-2-2-22-222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i-220000000000000000000000000000000000000000000000000000
χ782-2-22-2-222222222-2-2-2-2-2-222-2-2-22-22−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i-220000000000000000000000000000000000000000000000000000
χ792-2-22-2-22222-2-2-2-22222-2-222-2-22-22-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-220000000000000000000000000000000000000000000000000000
χ802-2-22-2-22222-2-2-2-22222-2-222-2-22-22-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-220000000000000000000000000000000000000000000000000000
χ812-2-22-2-222-2-222-2-2-2-22222-2-2222-2-220000000000000000-22000000000000000022-2-2-2-22222-2-2-2-22200000000000000000000
χ822-2-22-2-222-2-222-2-2-2-22222-2-2222-2-220000000000000000-220000000000000000-2-22222-2-2-2-22222-2-200000000000000000000
χ832-2-22-2-222-2-222-2-2-2-222-2-22222-222-200000000000000002-222-2-2-2-22222-2-2-2-222000000000000000000000000000000000000
χ842-2-22-2-222-2-222-2-2-2-222-2-22222-222-200000000000000002-2-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000
χ852-2-22-2-222-2-2-2-22222-2-222-2-222-222-20000000000000000-22000000000000000022-2-2-2-222-2-22222-2-200000000000000000000
χ862-2-22-2-222-2-2-2-22222-2-222-2-222-222-20000000000000000-220000000000000000-2-22222-2-222-2-2-2-22200000000000000000000
χ872-2-22-2-222-2-2-2-22222-2-2-2-222222-2-2200000000000000002-222-2-2-2-222-2-22222-2-2000000000000000000000000000000000000
χ882-2-22-2-222-2-2-2-22222-2-2-2-222222-2-2200000000000000002-2-2-22222-2-222-2-2-2-222000000000000000000000000000000000000
χ89444-4-4-44-400000000004-44-40000000000000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ90444-4-4-44-400000000004-44-4000000000000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ91444-4-4-44-40000000000-44-44000000000000000000000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ92444-4-4-44-40000000000-44-4400000000000000000000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ934-4-4-4444-400000000004-4-4400000000000000000000000000000000000000000000000000000000000022−22−2222000000000000
χ944-4-4-4444-400000000004-4-44000000000000000000000000000000000000000000000000000000000000−222222−22000000000000
χ954-4-4-4444-40000000000-444-40000000000000000000000000000000000000000000000000000000022−22−22220000000000000000
χ964-4-4-4444-40000000000-444-400000000000000000000000000000000000000000000000000000000−222222−220000000000000000
χ9788-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-88-88-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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