Finite Group Databasebeta

← Group #10702242

Character table — Group #10702242

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order12222222222222223444444446666666666666668888888812121212121212122424242424242424242424242424242422224444666666661212121212121212444444448888888844444444
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
χ9111111-1-1-1-1-11-1-11-11111-1-1-1-11111111-1-1-1-1-1-1-11-1iiii−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−iii−i−iii−i−i1111-1-1-1-1ii−i−i11-1-1
χ10111111-1-1-1-1-11-1-11-11111-1-1-1-11111111-1-1-1-1-1-1-11-1iiii−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−i−iii−i−iii-1-1-1-11111−i−iii-1-111
χ11111111-1-1-1-1-11-1-11-11111-1-1-1-11111111-1-1-1-1-1-1-11-1iiii−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−iiiiiii−i−iii−i−i1111-1-1-1-1−i−iii-1-111
χ12111111-1-1-1-1-11-1-11-11111-1-1-1-11111111-1-1-1-1-1-1-11-1iiii−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−i−iii−i−iii-1-1-1-11111ii−i−i11-1-1
χ13111111-1-1-1-1-11-1-11-11111-1-1-1-11111111-1-1-1-1-1-1-11-1−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−iiiiiii−i−iii−i−i-1-1-1-11111ii−i−i-1-111
χ14111111-1-1-1-1-11-1-11-11111-1-1-1-11111111-1-1-1-1-1-1-11-1−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−i−iii−i−iii1111-1-1-1-1−i−iii11-1-1
χ15111111-1-1-1-1-11-1-11-11111-1-1-1-11111111-1-1-1-1-1-1-11-1−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−iii−i−iii−i−i-1-1-1-11111−i−iii11-1-1
χ16111111-1-1-1-1-11-1-11-11111-1-1-1-11111111-1-1-1-1-1-1-11-1−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−i−iii−i−iii1111-1-1-1-1ii−i−i-1-111
χ1722222222222222222-2-2-2-2-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000002222-2-2-2-20000000000000000
χ1822222222222222222-2-2-2-2-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-2-2-222220000000000000000
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
χ23222222-2-2-2-2-22-2-22-22-2-2-22222-2222222-2-2-2-2-2-2-22-200000000-2-2-2-2222200000000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ24222222-2-2-2-2-22-2-22-22-2-2-22222-2222222-2-2-2-2-2-2-22-200000000-2-2-2-222220000000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ25222222-2-2-2-2-22-2-22-2-1222-2-2-2-22-1-1-1-1-1-11111111-112i2i2i2i−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
χ26222222-2-2-2-2-22-2-22-2-1222-2-2-2-22-1-1-1-1-1-11111111-112i2i2i2i−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
χ27222222-2-2-2-2-22-2-22-2-1222-2-2-2-22-1-1-1-1-1-11111111-11−2i−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
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χ292222-2-2222-2-2-2-22-2-2200000000222-2-2-2222-2-2-2-2-2222−2−222−2−2000000002222−2−2−2−22222−2−2−2−20000000000000000000000002i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i200000000
χ302222-2-2222-2-2-2-22-2-2200000000222-2-2-2222-2-2-2-2-2222−2−222−2−2000000002222−2−2−2−22222−2−2−2−2000000000000000000000000−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i200000000
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χ322222-2-2222-2-2-2-22-2-2200000000222-2-2-2222-2-2-2-2-22−2−222−2−22200000000−2−2−2−22222−2−2−2−22222000000000000000000000000−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i200000000
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χ342222-2-2-2-2-222-22-2-22200000000222-2-2-2-2-2-22222-2-2−i2−i2i2i2i2i2−i2−i200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2000000000000000000000000-222-20000i2i2−i2−i2−i2−i2i2i200000000
χ352222-2-2-2-2-222-22-2-22200000000222-2-2-2-2-2-22222-2-2i2i2−i2−i2−i2−i2i2i200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i20000000000000000000000002-2-220000i2i2−i2−i2−i2−i2i2i200000000
χ362222-2-2-2-2-222-22-2-22200000000222-2-2-2-2-2-22222-2-2i2i2−i2−i2−i2−i2i2i200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2000000000000000000000000-222-20000−i2−i2i2i2i2i2−i2−i200000000
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χ4922-2-22-2-2-22-2-2222-22-122-2-2-222-2-111-11111-111-1-1-1-100000000-1-11111-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i32-2-220000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3000000000000000000000000
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χ762-22-2-22-22-22-2222-2-2-1-22-22-2-2221-1111-11-11-11-11-1-1-222-22-2-221-11-1-111-11-11-1-11-11-11-111-11-100000000i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3000000000000000000000000
χ772-2-22-2-22-2-2-222222-222-2-22-22-22-2-22-22-22-2-2-222-222000000002-2-222-22-20000000000000000000000000000000000000000000000000000000000002-22-2
χ782-2-22-2-22-2-2-222222-222-2-22-22-22-2-22-22-22-2-2-222-222000000002-2-222-22-2000000000000000000000000000000000000000000000000000000000000-22-22
χ792-2-22-2-22-2-2-222222-22-222-22-22-2-2-22-22-22-2-2-222-22200000000-222-2-22-22000000000000000000002-22-2000000002-2-222-2-22000000000000000000000000
χ802-2-22-2-22-2-2-222222-22-222-22-22-2-2-22-22-22-2-2-222-22200000000-222-2-22-2200000000000000000000-22-2200000000-222-2-222-2000000000000000000000000
χ812-2-22-2-22-2-2-222222-2-1-222-22-22-211-11-11-1111-1-11-1-1000000001-1-111-11-1−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i300002-22-2−i3i3i3−i3−i3i3i3−i3-111-1-111-1000000000000000000000000
χ822-2-22-2-22-2-2-222222-2-1-222-22-22-211-11-11-1111-1-11-1-1000000001-1-111-11-1−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i30000-22-22i3−i3−i3i3i3−i3−i3i31-1-111-1-11000000000000000000000000
χ832-2-22-2-22-2-2-222222-2-1-222-22-22-211-11-11-1111-1-11-1-1000000001-1-111-11-1i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i300002-22-2i3−i3−i3i3i3−i3−i3i3-111-1-111-1000000000000000000000000
χ842-2-22-2-22-2-2-222222-2-1-222-22-22-211-11-11-1111-1-11-1-1000000001-1-111-11-1i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i30000-22-22−i3i3i3−i3−i3i3i3−i31-1-111-1-11000000000000000000000000
χ852-2-22-2-2-2222-22-2-22222-2-2-22-222-2-22-22-2-2222-2-222-2000000002-2-22-22-220000000000000000000000000000000000000000000000000000000000002-2-22
χ862-2-22-2-2-2222-22-2-22222-2-2-22-222-2-22-22-2-2222-2-222-2000000002-2-22-22-22000000000000000000000000000000000000000000000000000000000000-222-2
χ872-2-22-2-2-2222-22-2-2222-2222-22-2-2-2-22-22-2-2222-2-222-200000000-222-22-22-2000000000000000000002i−2i−2i2i000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ882-2-22-2-2-2222-22-2-2222-2222-22-2-2-2-22-22-2-2222-2-222-200000000-222-22-22-200000000000000000000−2i2i2i−2i00000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ892-2-22-2-2-2222-22-2-222-1-2222-22-2-211-11-111-1-1-111-1-11000000001-1-11-11-113−3−33−333−3−333−33−3−3300002i−2i−2i2i−i3i3i3−i3i3−i3−i3i3−iii−ii−i−ii000000000000000000000000
χ902-2-22-2-2-2222-22-2-222-1-2222-22-2-211-11-111-1-1-111-1-11000000001-1-11-11-113−3−33−333−3−333−33−3−330000−2i2i2i−2ii3−i3−i3i3−i3i3i3−i3i−i−ii−iii−i000000000000000000000000
χ912-2-22-2-2-2222-22-2-222-1-2222-22-2-211-11-111-1-1-111-1-11000000001-1-11-11-11−333−33−3−333−3−33−333−300002i−2i−2i2ii3−i3−i3i3−i3i3i3−i3−iii−ii−i−ii000000000000000000000000
χ922-2-22-2-2-2222-22-2-222-1-2222-22-2-211-11-111-1-1-111-1-11000000001-1-11-11-11−333−33−3−333−3−33−333−30000−2i2i2i−2i−i3i3i3−i3i3−i3−i3i3i−i−ii−iii−i000000000000000000000000
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
χ94444444-4-4-4-4-44-4-44-4-2-4-4-44444-4-2-2-2-2-2-22222222-22000000002222-2-2-2-20000000000000000000000000000000000000000000000000000000000000000
χ954444-4-4444-4-4-4-44-4-4-200000000-2-2-2222-2-2-222222-22222−22−222222−22−2200000000−2−2−2−22222−2−2−2−22222000000000000000000000000000000000000000000000000
χ964444-4-4444-4-4-4-44-4-4-200000000-2-2-2222-2-2-222222-2−22−222222−22−222222000000002222−2−2−2−22222−2−2−2−2000000000000000000000000000000000000000000000000
χ974444-4-4-4-4-444-44-4-44-200000000-2-2-2222222-2-2-2-222−2i2−2i22i22i22i22i2−2i2−2i200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2000000000000000000000000000000000000000000000000
χ984444-4-4-4-4-444-44-4-44-200000000-2-2-2222222-2-2-2-2222i22i2−2i2−2i2−2i2−2i22i22i200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2000000000000000000000000000000000000000000000000
χ9944-4-44-444-4444-4-4-4-4-2-4-44-4-4444-222-222-2-22-2-222-220000000022-2-222-2-20000000000000000000000000000000000000000000000000000000000000000
χ10044-4-44-4-4-44-4-4444-44-2-4-4444-4-44-222-22222-222-2-2-2-20000000022-2-2-2-2220000000000000000000000000000000000000000000000000000000000000000
χ10144-4-4-4444-4-4-4-44-4444000000004-4-4-44444-4-4-444-4-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10244-4-4-4444-4-4-4-44-444-200000000-2222-2-2-2-2222-2-222000000000000000066−6−6−6−66666−6−6−6−666000000000000000000000000000000000000000000000000
χ10344-4-4-4444-4-4-4-44-444-200000000-2222-2-2-2-2222-2-2220000000000000000−6−66666−6−6−6−66666−6−6000000000000000000000000000000000000000000000000
χ10444-4-4-44-4-4444-4-444-44000000004-4-4-444-4-4444-4-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10544-4-4-44-4-4444-4-444-4-200000000-2222-2-222-2-2-2222-20000000000000000i6i6−i6−i6−i6−i6i6i6−i6−i6i6i6i6i6−i6−i6000000000000000000000000000000000000000000000000
χ10644-4-4-44-4-4444-4-444-4-200000000-2222-2-222-2-2-2222-20000000000000000−i6−i6i6i6i6i6−i6−i6i6i6−i6−i6−i6−i6i6i6000000000000000000000000000000000000000000000000
χ1074-44-44-44-444-4-44-44-4-2000000002-22-2-22-22-2-22-2222−2i22i2−2i22i2−2i22i2−2i22i200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000000000000000000000000000
χ1084-44-44-44-444-4-44-44-4-2000000002-22-2-22-22-2-22-22222i2−2i22i2−2i22i2−2i22i2−2i200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000000000000000000000000000
χ1094-44-44-4-44-4-44-4-4444-2000000002-22-2-222-222-22-22-222−2222−22−2222−222200000000−22−22−22−222−22−22−22−2000000000000000000000000000000000000000000000000
χ1104-44-44-4-44-4-44-4-4444-2000000002-22-2-222-222-22-22-2−2222−222222−2222−22000000002−22−22−22−2−22−22−22−22000000000000000000000000000000000000000000000000
χ1114-44-4-444-44-444-4-4-44-24-444-4-44-42-2222-2-22-22-22-2-2200000000-22-22-222-20000000000000000000000000000000000000000000000000000000000000000
χ1124-44-4-44-44-44-4444-4-4-24-44-444-4-42-2222-22-22-22-22-2-200000000-22-222-2-220000000000000000000000000000000000000000000000000000000000000000
χ1134-4-44444-4-44-4-4-44-44400000000-4-444-444-4-44-4-44-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1144-4-44444-4-44-4-4-44-44-20000000022-2-22-2-222-222-22-20000000000000000i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6000000000000000000000000000000000000000000000000
χ1154-4-44444-4-44-4-4-44-44-20000000022-2-22-2-222-222-22-20000000000000000−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6000000000000000000000000000000000000000000000000
χ1164-4-4444-444-44-44-4-4-4400000000-4-444-44-444-444-4-4-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1174-4-4444-444-44-44-4-4-4-20000000022-2-22-22-2-22-2-222200000000000000006−6−666−6−66−666−6−666−6000000000000000000000000000000000000000000000000
χ1184-4-4444-444-44-44-4-4-4-20000000022-2-22-22-2-22-2-22220000000000000000−666−6−666−66−6−666−6−66000000000000000000000000000000000000000000000000
χ1194-4-44-4-44-4-4-444444-4-24-4-44-44-4422-22-22-2222-2-22-2-200000000-222-2-22-220000000000000000000000000000000000000000000000000000000000000000
χ1204-4-44-4-4-4444-44-4-444-24-4-4-44-44422-22-222-2-2-222-2-2200000000-222-22-22-20000000000000000000000000000000000000000000000000000000000000000

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