Finite Group Databasebeta

← Group #10701896

Character table — Group #10701896

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order12222222222222223444444446666666666666668888888812121212121212122424242424242424242424242424242422224444666666661212121212121212444444448888888822224444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111-1-1-1-1-1-11-111-111111-1-1-1-1111111-1-1-1-1-1-1-11-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i
χ1011111-1-1-1-1-1-11-111-111111-1-1-1-1111111-1-1-1-1-1-1-11-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii
χ1111111-1-1-1-1-1-11-111-111111-1-1-1-1111111-1-1-1-1-1-1-11-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii
χ1211111-1-1-1-1-1-11-111-111111-1-1-1-1111111-1-1-1-1-1-1-11-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i
χ1311111-1-1-1-1-1-11-111-111111-1-1-1-1111111-1-1-1-1-1-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii
χ1411111-1-1-1-1-1-11-111-111111-1-1-1-1111111-1-1-1-1-1-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i
χ1511111-1-1-1-1-1-11-111-111111-1-1-1-1111111-1-1-1-1-1-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i
χ1611111-1-1-1-1-1-11-111-111111-1-1-1-1111111-1-1-1-1-1-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii
χ1722222222222222222-2-2-2-2-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000022-2-222-2-20000000000000000
χ1822222222222222222-2-2-2-2-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-222-2-2220000000000000000
χ192222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ202222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ212222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ222222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ2322222-2-2-2-2-2-22-222-22-2-2-2-22222222222-2-2-2-2-2-2-22-200000000-2-2-2-22222000000000000000000000000000000000000000022-2-2-2-2220000000000000000
χ2422222-2-2-2-2-2-22-222-22-2-2-2-22222222222-2-2-2-2-2-2-22-200000000-2-2-2-222220000000000000000000000000000000000000000-2-22222-2-20000000000000000
χ2522222-2-2-2-2-2-22-222-2-12222-2-2-2-2-1-1-1-1-1-11111111-112i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii22-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii000000000000000000000000
χ2622222-2-2-2-2-2-22-222-2-12222-2-2-2-2-1-1-1-1-1-11111111-112i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i000000000000000000000000
χ2722222-2-2-2-2-2-22-222-2-12222-2-2-2-2-1-1-1-1-1-11111111-11−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i22-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i000000000000000000000000
χ2822222-2-2-2-2-2-22-222-2-12222-2-2-2-2-1-1-1-1-1-11111111-11−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii000000000000000000000000
χ29222-2-22222-2-22-2-2-2-2222-2-22-22-222-2-2-2-22222-2-2-22-20000000022-2-22-2-220000000000000000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ30222-2-22222-2-22-2-2-2-2222-2-22-22-222-2-2-2-22222-2-2-22-20000000022-2-22-2-22000000000000000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ31222-2-22222-2-22-2-2-2-22-2-222-22-2222-2-2-2-22222-2-2-22-22i2i−2i−2i2i2i−2i−2i-2-222-222-22i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000000000000000
χ32222-2-22222-2-22-2-2-2-22-2-222-22-2222-2-2-2-22222-2-2-22-2−2i−2i2i2i−2i−2i2i2i-2-222-222-2−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000000000
χ33222-2-22222-2-22-2-2-2-2-1-2-222-22-22-1-11111-1-1-1-1111-112i2i−2i−2i2i2i−2i−2i11-1-11-1-11−i−i−i−iiiii−i−i−i−iiiii00000000−i3−i3i3i3−i3−i3i3i333−3−333−3−3000000000000000000000000
χ34222-2-22222-2-22-2-2-2-2-1-2-222-22-22-1-11111-1-1-1-1111-112i2i−2i−2i2i2i−2i−2i11-1-11-1-11−i−i−i−iiiii−i−i−i−iiiii00000000i3i3−i3−i3i3i3−i3−i3−3−333−3−333000000000000000000000000
χ35222-2-22222-2-22-2-2-2-2-1-2-222-22-22-1-11111-1-1-1-1111-11−2i−2i2i2i−2i−2i2i2i11-1-11-1-11iiii−i−i−i−iiiii−i−i−i−i00000000−i3−i3i3i3−i3−i3i3i3−3−333−3−333000000000000000000000000
χ36222-2-22222-2-22-2-2-2-2-1-2-222-22-22-1-11111-1-1-1-1111-11−2i−2i2i2i−2i−2i2i2i11-1-11-1-11iiii−i−i−i−iiiii−i−i−i−i00000000i3i3−i3−i3i3i3−i3−i333−3−333−3−3000000000000000000000000
χ37222-2-2-2-2-2-22222-2-22222-2-2-22-2222-2-2-2-2-2-2-2-2222220000000022-2-2-222-200000000000000000000000000000000000000000000000022-2-2-2-22200000000
χ38222-2-2-2-2-2-22222-2-22222-2-2-22-2222-2-2-2-2-2-2-2-2222220000000022-2-2-222-2000000000000000000000000000000000000000000000000-2-22222-2-200000000
χ39222-2-2-2-2-2-22222-2-222-2-2222-22-222-2-2-2-2-2-2-2-22222222-2-2-2-222-2-2222-2-222222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ40222-2-2-2-2-2-22222-2-222-2-2222-22-222-2-2-2-2-2-2-2-222222-2-22222-2-2-2-2222-2-22-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000
χ41222-2-2-2-2-2-22222-2-22-1-2-2222-22-2-1-111111111-1-1-1-1-122-2-2-2-22211-1-1-111-1-1-1-1-111111111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3000000000000000000000000
χ42222-2-2-2-2-2-22222-2-22-1-2-2222-22-2-1-111111111-1-1-1-1-122-2-2-2-22211-1-1-111-1-1-1-1-111111111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3000000000000000000000000
χ43222-2-2-2-2-2-22222-2-22-1-2-2222-22-2-1-111111111-1-1-1-1-1-2-22222-2-211-1-1-111-11111-1-1-1-1-1-1-1-1111100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000000000000000000000000
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χ5122-22-2-2-222-2-2-222-222000000002-222-2-2-2-222-2-22-22−22−222−22−200000000−2−222−2−22222−2−222−2−2000000000000000000000000002-200-22−22−222−22−200000000
χ5222-22-2-2-222-2-2-222-222000000002-222-2-2-2-222-2-22-22−22−222−22−200000000−2−222−2−22222−2−222−2−200000000000000000000000000-22002-22−22−2−22−2200000000
χ5322-2-2222-2-2-2-2-22-2222000000002-2-2-22222-2-2-2-22-222−2−222−2−220000000022−2−2−2−22222−2−2−2−2220000000000000000000000002-2002-2002−2−222−2−2200000000
χ5422-2-2222-2-2-2-2-22-2222000000002-2-2-22222-2-2-2-22-222−2−222−2−220000000022−2−2−2−22222−2−2−2−222000000000000000000000000-2200-2200−222−2−222−200000000
χ5522-2-2222-2-2-2-2-22-2222000000002-2-2-22222-2-2-2-22-22−222−2−222−200000000−2−22222−2−2−2−22222−2−20000000000000000000000002-2002-200−222−2−222−200000000
χ5622-2-2222-2-2-2-2-22-2222000000002-2-2-22222-2-2-2-22-22−222−2−222−200000000−2−22222−2−2−2−22222−2−2000000000000000000000000-2200-22002−2−222−2−2200000000
χ5722-2-22-2-22222-2-2-22-22000000002-2-2-222-2-22222-2-2-2−i2i2i2−i2i2−i2−i2i200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000000000002-200-2200−i2i2i2−i2i2−i2−i2i200000000
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χ632-2-2222-22-22-222-2-2-22-22-22-2-222-2-22-22-22-22-22-2-22200000000-22-22-2-222000000000000000000002-22-2000000002-22-22-22-2000000000000000000000000
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χ762-2-222-22-22-222-2-2-22-1-22-2222-2-211-11-111-11-11-1-1-11000000001-11-1-1-111−33−33−33−333−33−33−33−30000−2i2i2i−2i−i3i3−i3i3i3−i3i3−i3i−ii−i−ii−ii000000000000000000000000
χ772-2-2-2-22-22-2-222-222222-2-222-2-22-2-2-22-222-22-2-2222-2000000002-2-222-22-200000000000000002-22-200002-2-222-2-2200000000000000000000000000000000
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χ792-2-2-2-22-22-2-222-22222-222-2-222-2-2-2-22-222-22-2-2222-200000000-222-2-22-22000000000000000000000000000000000000000000000000000000002-22-20000
χ802-2-2-2-22-22-2-222-22222-222-2-222-2-2-2-22-222-22-2-2222-200000000-222-2-22-2200000000000000000000000000000000000000000000000000000000-22-220000
χ812-2-2-2-22-22-2-222-2222-12-2-222-2-22111-11-1-11-111-1-1-1100000000-111-1-11-113−33−3−33−333−33−3−33−332-22-20000-111-1-111-13−3−333−3−33000000000000000000000000
χ822-2-2-2-22-22-2-222-2222-12-2-222-2-22111-11-1-11-111-1-1-1100000000-111-1-11-113−33−3−33−333−33−3−33−33-22-2200001-1-111-1-11−333−3−333−3000000000000000000000000
χ832-2-2-2-22-22-2-222-2222-12-2-222-2-22111-11-1-11-111-1-1-1100000000-111-1-11-11−33−333−33−3−33−333−33−32-22-20000-111-1-111-1−333−3−333−3000000000000000000000000
χ842-2-2-2-22-22-2-222-2222-12-2-222-2-22111-11-1-11-111-1-1-1100000000-111-1-11-11−33−333−33−3−33−333−33−3-22-2200001-1-111-1-113−3−333−3−33000000000000000000000000
χ852-2-2-2-2-22-222-22222-222-2-22-222-2-2-2-22-22-22-222-2-222000000002-2-22-22-2200000000000000002-2-2200002-2-22-222-200000000000000000000000000000000
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χ872-2-2-2-2-22-222-22222-22-222-22-2-22-2-2-22-22-22-222-2-22200000000-222-22-22-2000000000000000000000000000000000000000000000000000000002-2-220000
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χ912-2-2-2-2-22-222-22222-2-12-2-22-222-2111-11-11-11-1-111-1-100000000-111-11-11-1i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3i3−i3i3−i32-2-220000-111-11-1-11i3−i3−i3i3−i3i3i3−i3000000000000000000000000
χ922-2-2-2-2-22-222-22222-2-12-2-22-222-2111-11-11-11-1-111-1-100000000-111-11-11-1i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3-222-200001-1-11-111-1−i3i3i3−i3i3−i3−i3i3000000000000000000000000
χ934444444444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000222222220000000000000000000000000000000000000000000000000000000000000000
χ9444444-4-4-4-4-4-44-444-4-2-4-4-4-44444-2-2-2-2-2-22222222-22000000002222-2-2-2-20000000000000000000000000000000000000000000000000000000000000000
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χ96444-4-4-4-4-4-44444-4-44-244-4-4-44-44-2-222222222-2-2-2-2-200000000-2-2222-2-220000000000000000000000000000000000000000000000000000000000000000
χ9744-44-444-4-444-4-44-4-4-200000000-22-2-222-2-222-2-2222−2i22i2−2i22i2−2i22i2−2i22i200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000000000000000000000000000
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χ9944-44-4-4-444-4-4-444-44-200000000-22-2-22222-2-222-22-222−2222−22−2222−222200000000−2−222−2−22222−2−222−2−2000000000000000000000000000000000000000000000000
χ10044-44-4-4-444-4-4-444-44-200000000-22-2-22222-2-222-22-2−2222−222222−2222−220000000022−2−222−2−2−2−222−2−222000000000000000000000000000000000000000000000000
χ10144-4-4444-4-4-4-4-44-444-200000000-2222-2-2-2-22222-22-222−22−222222−22−222200000000−2−22222−2−2−2−22222−2−2000000000000000000000000000000000000000000000000
χ10244-4-4444-4-4-4-4-44-444-200000000-2222-2-2-2-22222-22-2−222222−22−222222−220000000022−2−2−2−22222−2−2−2−222000000000000000000000000000000000000000000000000
χ10344-4-44-4-44444-4-4-44-4-200000000-2222-2-222-2-2-2-2222−2i22i22i2−2i22i2−2i2−2i22i200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000000000000000000000000000
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χ1054-444-44-4-444-4-4-4-444400000000-444-4-444-4-444-44-4-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1064-444-44-4-444-4-4-4-444-2000000002-2-222-2-222-2-22-22200000000000000006−6−666−6−666−6−666−6−66000000000000000000000000000000000000000000000000
χ1074-444-44-4-444-4-4-4-444-2000000002-2-222-2-222-2-22-2220000000000000000−666−6−666−6−666−6−666−6000000000000000000000000000000000000000000000000
χ1084-444-4-444-4-44-44-44-4400000000-444-4-44-444-4-44-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1094-444-4-444-4-44-44-44-4-2000000002-2-222-22-2-222-222-20000000000000000i6−i6−i6i6i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6000000000000000000000000000000000000000000000000
χ1104-444-4-444-4-44-44-44-4-2000000002-2-222-22-2-222-222-20000000000000000−i6i6i6−i6−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6000000000000000000000000000000000000000000000000
χ1114-44-444-4-44-44-444-4-4400000000-44-444-44-4-44-44-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1124-44-444-4-44-44-444-4-4-2000000002-22-2-22-222-22-222-20000000000000000i6−i6−i6i6−i6i6i6−i6i6−i6−i6i6−i6i6i6−i6000000000000000000000000000000000000000000000000
χ1134-44-444-4-44-44-444-4-4-2000000002-22-2-22-222-22-222-20000000000000000−i6i6i6−i6i6−i6−i6i6−i6i6i6−i6i6−i6−i6i6000000000000000000000000000000000000000000000000
χ1144-44-44-444-44-4-4-44-44400000000-44-444-4-444-44-44-4-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1154-44-44-444-44-4-4-44-44-2000000002-22-2-222-2-22-22-22200000000000000006−6−66−666−6−666−66−6−66000000000000000000000000000000000000000000000000
χ1164-44-44-444-44-4-4-44-44-2000000002-22-2-222-2-22-22-2220000000000000000−666−66−6−666−6−66−666−6000000000000000000000000000000000000000000000000
χ1174-4-4444-44-44-444-4-4-4-24-44-444-4-422-22-22-22-22-222-2-200000000-22-22-2-2220000000000000000000000000000000000000000000000000000000000000000
χ1184-4-444-44-44-444-4-4-44-24-44-4-4-44422-22-222-22-22-2-2-2200000000-22-2222-2-20000000000000000000000000000000000000000000000000000000000000000
χ1194-4-4-4-44-44-4-444-4444-2-444-4-444-4222-22-2-22-222-2-2-22000000002-2-222-22-20000000000000000000000000000000000000000000000000000000000000000
χ1204-4-4-4-4-44-444-44444-4-2-444-44-4-44222-22-22-22-2-222-2-2000000002-2-22-22-220000000000000000000000000000000000000000000000000000000000000000

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