Finite Group Databasebeta

← Group #206152

Character table — Group #206152

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222244444444444444448888888888888888444488888888888888888888888888888888888888882222224444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1111111-1-1
χ911111111-1-1-1-1111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111
χ1011111111-1-1-1-1111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1
χ1111111111-1-1-1-1111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1
χ1211111111-1-1-1-1111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111
χ1311111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-111-1-1
χ1411111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-111
χ1511111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111
χ1611111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1
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χ181-1-111-11-111-1-111-1-11111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1iiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-11−ii-11−ii−ii−ii
χ191-1-111-11-111-1-111-1-11111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1iiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii1-11-1-11−ii-11i−ii−i−ii
χ201-1-111-11-111-1-111-1-11111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1iiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-11-111-1i−i1-1−ii−iii−i
χ211-1-111-11-111-1-111-1-11111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-1−ii1-1−ii−ii−ii
χ221-1-111-11-111-1-111-1-11111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-11i−i-11i−ii−ii−i
χ231-1-111-11-111-1-111-1-11111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−i−i−iiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i1-11-1-11i−i-11−ii−iii−i
χ241-1-111-11-111-1-111-1-11111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−i−i−iiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-11-111-1−ii1-1i−ii−i−ii
χ251-1-111-11-1-1-11111-1-111-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1-111-1−ii-11i−i−iii−i
χ261-1-111-11-1-1-11111-1-111-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-111-1-11i−i1-1−iii−i−ii
χ271-1-111-11-1-1-11111-1-111-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i1-1-11-11i−i1-1i−i−ii−ii
χ281-1-111-11-1-1-11111-1-111-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-111-11-1−ii-11−iii−ii−i
χ291-1-111-11-1-1-11111-1-111-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1-111-1i−i-11−iii−i−ii
χ301-1-111-11-1-1-11111-1-111-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-111-1-11−ii1-1i−i−iii−i
χ311-1-111-11-1-1-11111-1-111-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111iiii−i−i−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii1-1-11-11−ii1-1−iii−ii−i
χ321-1-111-11-1-1-11111-1-111-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111iiii−i−i−i−i-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-111-11-1i−i-11i−i−ii−ii
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χ3422222222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-222222-22-2-2-222-2-222000000000000000000000000000000000000000000000000
χ35222222222222-2-222-2-2-2-2-2-222-2-2-2-20000000000000000-22-220000000022-2-222-2-222-2-222-2-200000000000000000000000000000000
χ36222222222222-2-222-2-2-2-2-2-222-2-2-2-20000000000000000-22-2200000000-2-222-2-222-2-222-2-22200000000000000000000000000000000
χ37222222222222-2-2-2-2222222-2-2-2-2220000000000000000-2-2-2-200000000000000000000000022-2-222-2-222-2-222-2-20000000000000000
χ38222222222222-2-2-2-2222222-2-2-2-2220000000000000000-2-2-2-2000000000000000000000000-2-222-2-222-2-222-2-2220000000000000000
χ3922222222-2-2-2-222-2-2-2-22222-2-222-2-22222-2-2-2-22222-2-2-2-2-22-22-2-222-2-222000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-222-2-2-2-22222-2-222-2-2-2-2-2-22222-2-2-2-22222-22-2222-2-222-2-2000000000000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-222-2-2222222-2-2-2-200000000000000002-22-20000000022-2-222-2-2-2-222-2-22200000000000000000000000000000000
χ4222222222-2-2-2-2-2-222-2-2222222-2-2-2-200000000000000002-22-200000000-2-222-2-22222-2-222-2-200000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2220000000000000000222200000000000000000000000022-2-222-2-2-2-222-2-2220000000000000000
χ4422222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22200000000000000002222000000000000000000000000-2-222-2-22222-2-222-2-20000000000000000
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χ46222-2-2-22-22-22-200002-22-22-200002-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000i2−i2i2−i2i2−i2i2−i2−22−22−22−22−22−22−22−2200−2i2i00−2i2i00−2i2i00−2i2i0000000000000000
χ47222-2-2-22-22-22-200002-22-22-200002-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000−i2i2−i2i2−i2i2−i2i22−22−22−22−22−22−22−22−200−2i2i00−2i2i00−2i2i00−2i2i0000000000000000
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χ50222-2-2-22-22-22-20000-22-22-220000-22i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000i2−i2−i2i2i2−i2−i2i2−222−2−222−2−222−2−222−2−2i2i00−2i2i00−2i2i00−2i2i000000000000000000
χ51222-2-2-22-22-22-20000-22-22-220000-22−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000−i2i2i2−i2−i2i2i2−i22−2−222−2−222−2−222−2−22−2i2i00−2i2i00−2i2i00−2i2i000000000000000000
χ52222-2-2-22-22-22-20000-22-22-220000-22−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000−i2i2i2−i2−i2i2i2−i2−222−2−222−2−222−2−222−22i−2i002i−2i002i−2i002i−2i000000000000000000
χ53222-2-2-22-2-22-2200002-2-22-2200002-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000−i2i2−i2i2−i2i2−i2i22−22−22−22−2−22−22−22−22002i−2i002i−2i00−2i2i00−2i2i0000000000000000
χ54222-2-2-22-2-22-2200002-2-22-2200002-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000−i2i2−i2i2−i2i2−i2i2−22−22−22−222−22−22−22−200−2i2i00−2i2i002i−2i002i−2i0000000000000000
χ55222-2-2-22-2-22-2200002-2-22-2200002-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000i2−i2i2−i2i2−i2i2−i22−22−22−22−2−22−22−22−2200−2i2i00−2i2i002i−2i002i−2i0000000000000000
χ56222-2-2-22-2-22-2200002-2-22-2200002-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000i2−i2i2−i2i2−i2i2−i2−22−22−22−222−22−22−22−2002i−2i002i−2i00−2i2i00−2i2i0000000000000000
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χ622-2-222-22-222-2-22222-2-2-2-222-2-2-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i2-2-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ632-2-222-22-222-2-2-2-2222222-2-2-2-222-2-20000000000000000-2-2220000000000000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000
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χ662-2-222-22-222-2-2-2-2-2-2-2-2-2-2222222220000000000000000-222-200000000-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ672-2-222-22-2-2-2222222-2-222-2-2-2-2-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i-222-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ682-2-222-22-2-2-2222222-2-222-2-2-2-2-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i-222-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ692-2-222-22-2-2-222-2-22222-2-222-2-222-2-2000000000000000022-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ702-2-222-22-2-2-222-2-22222-2-222-2-222-2-2000000000000000022-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ712-2-222-22-2-2-222-2-2-2-2-2-222-2-222222200000000000000002-2-220000000022-2-2-2-222-2-22222-2-200000000000000000000000000000000
χ722-2-222-22-2-2-222-2-2-2-2-2-222-2-222222200000000000000002-2-2200000000-2-22222-2-222-2-2-2-22200000000000000000000000000000000
χ732-2-2-2-22222-2-2200002-22-2-220000-2222−2−222−2−2−2−222−2−22200002−22−2−22−222−22−2−22−222−22−2−22−22002-200-22002-200-220000000000000000
χ742-2-2-2-22222-2-2200002-22-2-220000-2222−2−222−2−2−2−222−2−22200002−22−2−22−22−22−222−22−2−22−222−22−200-22002-200-22002-20000000000000000
χ752-2-2-2-22222-2-2200002-22-2-220000-22−2−222−2−22222−2−222−2−20000−22−222−22−22−22−2−22−222−22−2−22−2200-22002-200-22002-20000000000000000
χ762-2-2-2-22222-2-2200002-22-2-220000-22−2−222−2−22222−2−222−2−20000−22−222−22−2−22−222−22−2−22−222−22−2002-200-22002-200-220000000000000000
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χ782-2-2-2-22222-2-220000-22-222-200002-222−2−2−2−222−2−22222−2−200002−2−22−222−2−222−22−2−22−222−22−2−22-22002-200-22002-2000000000000000000
χ792-2-2-2-22222-2-220000-22-222-200002-2−2−22222−2−222−2−2−2−2220000−222−22−2−222−2−22−222−22−2−22−222−2-22002-200-22002-2000000000000000000
χ802-2-2-2-22222-2-220000-22-222-200002-2−2−22222−2−222−2−2−2−2220000−222−22−2−22−222−22−2−22−222−22−2−222-200-22002-200-22000000000000000000
χ812-2-2-2-2222-222-200002-2-222-20000-2222−2−222−2−2−2−222−2−2220000−22−222−22−22−22−2−22−22−22−222−22−2002-200-2200-22002-20000000000000000
χ822-2-2-2-2222-222-200002-2-222-20000-2222−2−222−2−2−2−222−2−2220000−22−222−22−2−22−222−22−22−22−2−22−2200-22002-2002-200-220000000000000000
χ832-2-2-2-2222-222-200002-2-222-20000-22−2−222−2−22222−2−222−2−200002−22−2−22−222−22−2−22−22−22−222−22−200-22002-2002-200-220000000000000000
χ842-2-2-2-2222-222-200002-2-222-20000-22−2−222−2−22222−2−222−2−200002−22−2−22−22−22−222−22−22−22−2−22−22002-200-2200-22002-20000000000000000
χ852-2-2-2-2222-222-20000-222-2-2200002-222−2−2−2−222−2−22222−2−20000−222−22−2−222−2−22−222−2−222−22−2−222-200-2200-22002-2000000000000000000
χ862-2-2-2-2222-222-20000-222-2-2200002-222−2−2−2−222−2−22222−2−20000−222−22−2−22−222−22−2−222−2−22−222−2-22002-2002-200-22000000000000000000
χ872-2-2-2-2222-222-20000-222-2-2200002-2−2−22222−2−222−2−2−2−22200002−2−22−222−22−2−22−222−2−222−22−2−22-22002-2002-200-22000000000000000000
χ882-2-2-2-2222-222-20000-222-2-2200002-2−2−22222−2−222−2−2−2−22200002−2−22−222−2−222−22−2−222−2−22−222−22-200-2200-22002-2000000000000000000
χ8944-44-44-4-40000004-40000004-400002i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000000000000000000000000000
χ9044-44-44-4-40000004-40000004-40000−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000000000000000000000000000
χ9144-44-44-4-4000000-44000000-4400002i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000000000000000000000000000
χ9244-44-44-4-4000000-44000000-440000−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000000000000000000000000000
χ9344-4-44-4-4400004-400000000004-40000004-4-4400004-4-44000000000000000000000000000000000000000000000000000000000000
χ9444-4-44-4-4400004-400000000004-4000000-444-40000-444-4000000000000000000000000000000000000000000000000000000000000
χ9544-4-44-4-440000-440000000000-44004-4-4400004-4-440000000000000000000000000000000000000000000000000000000000000000
χ9644-4-44-4-440000-440000000000-4400-444-40000-444-40000000000000000000000000000000000000000000000000000000000000000
χ974-444-4-4-440000004-4000000-44000022−2222−22−2222−2222−2222−222222−2222−22000000000000000000000000000000000000000000000000000000000000
χ984-444-4-4-440000004-4000000-440000−2222−222222−2222−2222−2222−22−2222−2222000000000000000000000000000000000000000000000000000000000000
χ994-444-4-4-44000000-440000004-4000022−2222−2222−2222−22−2222−2222−2222−2222000000000000000000000000000000000000000000000000000000000000
χ1004-444-4-4-44000000-440000004-40000−2222−2222−2222−222222−2222−2222−2222−22000000000000000000000000000000000000000000000000000000000000
χ1014-44-444-4-400004-40000000000-440000004i−4i−4i4i0000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ1024-44-444-4-400004-40000000000-44000000−4i4i4i−4i00004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ1034-44-444-4-40000-4400000000004-4004i−4i−4i4i0000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000
χ1044-44-444-4-40000-4400000000004-400−4i4i4i−4i00004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000

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