Finite Group Databasebeta

← Group #225751

Character table — Group #225751

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111222222444411112222224444222244444488882222444444888822224444448888444488888816161616444488888816161616
order12442488888888224424888888884444448888888888888888888888888888888888882244248888888844444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1
χ3111111-1-1-1-111-1-1111111-1-1-1-111-1-1111111-1-1-1-111-1-1111111-1-1-1-111-1-1111111-1-1-1-111-1-1111111-1-1-1-111-1-1111111-1-1-1-111-1-1
χ4111111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ511-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i
χ611-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii
χ711-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii
χ811-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i
χ92222-2-2000000002222-2-2000000002222-2-2000000002222-2-2000000002222-2-2000000002222-2-2000000002222-2-200000000
χ1022-2-22-20000000022-2-22-20000000022-2-22-20000000022-2-22-20000000022-2-22-20000000022-2-22-20000000022-2-22-200000000
χ112-22i−2i00i2−i22−200002-22i−2i00i2−i22−200002-22i−2i00i2−i22−200002-22i−2i00i2−i22−200002-22i−2i00i2−i22−200002-22i−2i00i2−i22−200002-22i−2i00i2−i22−20000
χ122-22i−2i00−i2i2−2200002-22i−2i00−i2i2−2200002-22i−2i00−i2i2−2200002-22i−2i00−i2i2−2200002-22i−2i00−i2i2−2200002-22i−2i00−i2i2−2200002-22i−2i00−i2i2−220000
χ132-2−2i2i00i2−i2−2200002-2−2i2i00i2−i2−2200002-2−2i2i00i2−i2−2200002-2−2i2i00i2−i2−2200002-2−2i2i00i2−i2−2200002-2−2i2i00i2−i2−2200002-2−2i2i00i2−i2−220000
χ142-2−2i2i00−i2i22−200002-2−2i2i00−i2i22−200002-2−2i2i00−i2i22−200002-2−2i2i00−i2i22−200002-2−2i2i00−i2i22−200002-2−2i2i00−i2i22−200002-2−2i2i00−i2i22−20000
χ151111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ161111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ17111111-1-1-1-111-1-1111111-1-1-1-111-1-1111111-1-1-1-111-1-1111111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-111
χ18111111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ1911-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i-1-1111-1-1-111−ii−ii-1-1111-1-1-111−ii−ii
χ2011-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii-1-1111-1-1-111i−ii−i-1-1111-1-1-111i−ii−i
χ2111-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii-1-1111-111-1-1−iii−i-1-1111-111-1-1−iii−i
χ2211-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i-1-1111-111-1-1i−i−ii-1-1111-111-1-1i−i−ii
χ232222-2-2000000002222-2-2000000002222-2-2000000002222-2-2000000002222-2-200000000-2-2-2-22200000000-2-2-2-22200000000
χ2422-2-22-20000000022-2-22-20000000022-2-22-20000000022-2-22-20000000022-2-22-200000000-2-222-2200000000-2-222-2200000000
χ252-22i−2i00i2−i22−200002-22i−2i00i2−i22−200002-22i−2i00i2−i22−200002-22i−2i00i2−i22−200002-22i−2i00i2−i22−20000-22−2i2i00−i2i2−220000-22−2i2i00−i2i2−220000
χ262-22i−2i00−i2i2−2200002-22i−2i00−i2i2−2200002-22i−2i00−i2i2−2200002-22i−2i00−i2i2−2200002-22i−2i00−i2i2−220000-22−2i2i00i2−i22−20000-22−2i2i00i2−i22−20000
χ272-2−2i2i00i2−i2−2200002-2−2i2i00i2−i2−2200002-2−2i2i00i2−i2−2200002-2−2i2i00i2−i2−2200002-2−2i2i00i2−i2−220000-222i−2i00−i2i22−20000-222i−2i00−i2i22−20000
χ282-2−2i2i00−i2i22−200002-2−2i2i00−i2i22−200002-2−2i2i00−i2i22−200002-2−2i2i00−i2i22−200002-2−2i2i00−i2i22−20000-222i−2i00i2−i2−220000-222i−2i00i2−i2−220000
χ29111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ301111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111-1-1-1-111-1-1111111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111
χ32111111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1
χ3311-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i-1-1111-1-1-111−ii−ii-1-1111-1-1-111−ii−ii11-1-1-1111-1-1i−ii−i-1-1111-1-1-111−ii−ii
χ3411-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii-1-1111-1-1-111i−ii−i-1-1111-1-1-111i−ii−i11-1-1-1111-1-1−ii−ii-1-1111-1-1-111i−ii−i
χ3511-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii-1-1111-111-1-1−iii−i-1-1111-111-1-1−iii−i11-1-1-11-1-111i−i−ii-1-1111-111-1-1−iii−i
χ3611-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i-1-1111-111-1-1i−i−ii-1-1111-111-1-1i−i−ii11-1-1-11-1-111−iii−i-1-1111-111-1-1i−i−ii
χ372222-2-2000000002222-2-2000000002222-2-200000000-2-2-2-22200000000-2-2-2-222000000002222-2-200000000-2-2-2-22200000000
χ3822-2-22-20000000022-2-22-20000000022-2-22-200000000-2-222-2200000000-2-222-220000000022-2-22-200000000-2-222-2200000000
χ392-22i−2i00i2−i22−200002-22i−2i00i2−i22−200002-22i−2i00i2−i22−20000-22−2i2i00−i2i2−220000-22−2i2i00−i2i2−2200002-22i−2i00i2−i22−20000-22−2i2i00−i2i2−220000
χ402-22i−2i00−i2i2−2200002-22i−2i00−i2i2−2200002-22i−2i00−i2i2−220000-22−2i2i00i2−i22−20000-22−2i2i00i2−i22−200002-22i−2i00−i2i2−220000-22−2i2i00i2−i22−20000
χ412-2−2i2i00i2−i2−2200002-2−2i2i00i2−i2−2200002-2−2i2i00i2−i2−220000-222i−2i00−i2i22−20000-222i−2i00−i2i22−200002-2−2i2i00i2−i2−220000-222i−2i00−i2i22−20000
χ422-2−2i2i00−i2i22−200002-2−2i2i00−i2i22−200002-2−2i2i00−i2i22−20000-222i−2i00i2−i2−220000-222i−2i00i2−i2−2200002-2−2i2i00−i2i22−20000-222i−2i00i2−i2−220000
χ43111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111
χ441111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ45111111-1-1-1-111-1-1111111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1
χ46111111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-111
χ4711-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i11-1-1-1111-1-1i−ii−i-1-1111-1-1-111−ii−ii-1-1111-1-1-111−ii−ii-1-1111-1-1-111−ii−ii11-1-1-1111-1-1i−ii−i
χ4811-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii11-1-1-1111-1-1−ii−ii-1-1111-1-1-111i−ii−i-1-1111-1-1-111i−ii−i-1-1111-1-1-111i−ii−i11-1-1-1111-1-1−ii−ii
χ4911-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii11-1-1-11-1-111i−i−ii-1-1111-111-1-1−iii−i-1-1111-111-1-1−iii−i-1-1111-111-1-1−iii−i11-1-1-11-1-111i−i−ii
χ5011-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i11-1-1-11-1-111−iii−i-1-1111-111-1-1i−i−ii-1-1111-111-1-1i−i−ii-1-1111-111-1-1i−i−ii11-1-1-11-1-111−iii−i
χ512222-2-2000000002222-2-2000000002222-2-200000000-2-2-2-22200000000-2-2-2-22200000000-2-2-2-222000000002222-2-200000000
χ5222-2-22-20000000022-2-22-20000000022-2-22-200000000-2-222-2200000000-2-222-2200000000-2-222-220000000022-2-22-200000000
χ532-22i−2i00i2−i22−200002-22i−2i00i2−i22−200002-22i−2i00i2−i22−20000-22−2i2i00−i2i2−220000-22−2i2i00−i2i2−220000-22−2i2i00−i2i2−2200002-22i−2i00i2−i22−20000
χ542-22i−2i00−i2i2−2200002-22i−2i00−i2i2−2200002-22i−2i00−i2i2−220000-22−2i2i00i2−i22−20000-22−2i2i00i2−i22−20000-22−2i2i00i2−i22−200002-22i−2i00−i2i2−220000
χ552-2−2i2i00i2−i2−2200002-2−2i2i00i2−i2−2200002-2−2i2i00i2−i2−220000-222i−2i00−i2i22−20000-222i−2i00−i2i22−20000-222i−2i00−i2i22−200002-2−2i2i00i2−i2−220000
χ562-2−2i2i00−i2i22−200002-2−2i2i00−i2i22−200002-2−2i2i00−i2i22−20000-222i−2i00i2−i2−220000-222i−2i00i2−i2−220000-222i−2i00i2−i2−2200002-2−2i2i00−i2i22−20000
χ572222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000000000
χ582222222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000000000000000
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χ722222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000i2i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i20000000000000000000000000000
χ73222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-22200000000000000i2i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i20000000000000000000000000000
χ74222222-2-2-2-2-2-222-2-2-2-2-2-2222222-2-200000000000000i2i2i2i2i2i2−i2−i2−i2−i2−i2−i2i2i2−i2−i2−i2−i2−i2−i2i2i2i2i2i2i2−i2−i20000000000000000000000000000
χ7522-2-2-2222-2-22i−2i2i−2i-2-2222-2-2-222−2i2i−2i2i00000000000000i2i2−i2−i2−i2i2i2i2−i2−i2−22−22−i2−i2i2i2i2−i2−i2−i2i2i22−22−20000000000000000000000000000
χ7622-2-2-2222-2-2−2i2i−2i2i-2-2222-2-2-2222i−2i2i−2i00000000000000i2i2−i2−i2−i2i2i2i2−i2−i22−22−2−i2−i2i2i2i2−i2−i2−i2i2i2−22−220000000000000000000000000000
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χ7822-2-2-22-2-222−2i2i2i−2i-2-2222-222-2-22i−2i−2i2i00000000000000i2i2−i2−i2−i2i2−i2−i2i2i22−2−22−i2−i2i2i2i2−i2i2i2−i2−i2−222−20000000000000000000000000000
χ794444-4-400000000-4-4-4-44400000000000000000000002i22i22i22i2−2i2−2i200000000−2i2−2i2−2i2−2i22i22i2000000000000000000000000000000000000
χ8044-4-44-400000000-4-444-4400000000000000000000002i22i2−2i2−2i22i2−2i200000000−2i2−2i22i22i2−2i22i2000000000000000000000000000000000000
χ814-44i−4i002i2−2i222−220000-44−4i4i00−2i22i2−22220000000000000000002i2−2i2−222200-222i−2i0000−2i22i222−22002-2−2i2i00000000000000000000000000000000
χ824-44i−4i00−2i22i2−22220000-44−4i4i002i2−2i222−220000000000000000002i2−2i2−2222002-2−2i2i0000−2i22i222−2200-222i−2i00000000000000000000000000000000
χ834-4−4i4i002i2−2i2−22220000-444i−4i00−2i22i222−220000000000000000002i2−2i222−2200-22−2i2i0000−2i22i2−2222002-22i−2i00000000000000000000000000000000
χ844-4−4i4i00−2i22i222−220000-444i−4i002i2−2i2−22220000000000000000002i2−2i222−22002-22i−2i0000−2i22i2−222200-22−2i2i00000000000000000000000000000000
χ8522222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000−i2−i2−i2−i2−i2−i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2i2i2i2i2i2i2i2i2i2i20000000000000000000000000000
χ862222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000−i2−i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2i2i2i2i2i2i2i2i2i2i2−i2−i2−i2−i20000000000000000000000000000
χ87222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-22200000000000000−i2−i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i20000000000000000000000000000
χ88222222-2-2-2-2-2-222-2-2-2-2-2-2222222-2-200000000000000−i2−i2−i2−i2−i2−i2i2i2i2i2i2i2−i2−i2i2i2i2i2i2i2−i2−i2−i2−i2−i2−i2i2i20000000000000000000000000000
χ8922-2-2-2222-2-22i−2i2i−2i-2-2222-2-2-222−2i2i−2i2i00000000000000−i2−i2i2i2i2−i2−i2−i2i2i22−22−2i2i2−i2−i2−i2i2i2i2−i2−i2−22−220000000000000000000000000000
χ9022-2-2-2222-2-2−2i2i−2i2i-2-2222-2-2-2222i−2i2i−2i00000000000000−i2−i2i2i2i2−i2−i2−i2i2i2−22−22i2i2−i2−i2−i2i2i2i2−i2−i22−22−20000000000000000000000000000
χ9122-2-2-22-2-2222i−2i−2i2i-2-2222-222-2-2−2i2i2i−2i00000000000000−i2−i2i2i2i2−i2i2i2−i2−i22−2−22i2i2−i2−i2−i2i2−i2−i2i2i2−222−20000000000000000000000000000
χ9222-2-2-22-2-222−2i2i2i−2i-2-2222-222-2-22i−2i−2i2i00000000000000−i2−i2i2i2i2−i2i2i2−i2−i2−222−2i2i2−i2−i2−i2i2−i2−i2i2i22−2−220000000000000000000000000000
χ934444-4-400000000-4-4-4-4440000000000000000000000−2i2−2i2−2i2−2i22i22i2000000002i22i22i22i2−2i2−2i2000000000000000000000000000000000000
χ9444-4-44-400000000-4-444-440000000000000000000000−2i2−2i22i22i2−2i22i2000000002i22i2−2i2−2i22i2−2i2000000000000000000000000000000000000
χ954-44i−4i002i2−2i222−220000-44−4i4i00−2i22i2−2222000000000000000000−2i22i222−22002-2−2i2i00002i2−2i2−222200-222i−2i00000000000000000000000000000000
χ964-44i−4i00−2i22i2−22220000-44−4i4i002i2−2i222−22000000000000000000−2i22i222−2200-222i−2i00002i2−2i2−2222002-2−2i2i00000000000000000000000000000000
χ974-4−4i4i002i2−2i2−22220000-444i−4i00−2i22i222−22000000000000000000−2i22i2−2222002-22i−2i00002i2−2i222−2200-22−2i2i00000000000000000000000000000000
χ984-4−4i4i00−2i22i222−220000-444i−4i002i2−2i2−2222000000000000000000−2i22i2−222200-22−2i2i00002i2−2i222−22002-22i−2i00000000000000000000000000000000

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