Finite Group Databasebeta

← Group #10702243

Character table — Group #10702243

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order1222222222222222344444444666666666666666888888881212121212121212242424242424242424242424242424244444444412121212121212121212121212121212444444448888888822224444
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
χ9111111-1-1-1-1-11-1-1-111111-1-1-11-1111111-1-1-1-1-1-11-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−iiiii−i−i−i−i11-1-111-1-1
χ10111111-1-1-1-1-11-1-1-111111-1-1-11-1111111-1-1-1-1-1-11-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii−i−i−i−iiiii-1-111-1-111
χ11111111-1-1-1-1-11-1-1-111111-1-1-11-1111111-1-1-1-1-1-11-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−iiiii−i−i−i−i-1-111-1-111
χ12111111-1-1-1-1-11-1-1-111111-1-1-11-1111111-1-1-1-1-1-11-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii−i−i−i−iiiii11-1-111-1-1
χ13111111-1-1-1-1-11-1-1-111111-1-1-11-1111111-1-1-1-1-1-11-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−iii−i−i−i−i−i−iiiii11-1-1-1-111
χ14111111-1-1-1-1-11-1-1-111111-1-1-11-1111111-1-1-1-1-1-11-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−iii−i−iiiiiii−i−i−i−i-1-11111-1-1
χ15111111-1-1-1-1-11-1-1-111111-1-1-11-1111111-1-1-1-1-1-11-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−iii−i−i−i−i−i−iiiii-1-11111-1-1
χ16111111-1-1-1-1-11-1-1-111111-1-1-11-1111111-1-1-1-1-1-11-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii−i−iiiiiii−i−i−i−i11-1-1-1-111
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
χ23222222-2-2-2-2-22-2-2-222-2-2-2222-22222222-2-2-2-2-2-22-2-200000000-2-2-22222-200000000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ24222222-2-2-2-2-22-2-2-222-2-2-2222-22222222-2-2-2-2-2-22-2-200000000-2-2-22222-20000000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ25222222-2-2-2-2-22-2-2-22-1222-2-2-22-2-1-1-1-1-1-1111111-1112222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-1111111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000000000000000
χ26222222-2-2-2-2-22-2-2-22-1222-2-2-22-2-1-1-1-1-1-1111111-1112222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-111111111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000000000000000
χ27222222-2-2-2-2-22-2-2-22-1222-2-2-22-2-1-1-1-1-1-1111111-111-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i000000000000000000000000
χ28222222-2-2-2-2-22-2-2-22-1222-2-2-22-2-1-1-1-1-1-1111111-111-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii000000000000000000000000
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χ302222-2-2222-2-2-2-2-22-2200000000222-2-2-2222-2-2-2-22-2−i2−i2i2i2−i2−i2i2i200000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2000000000000000000000000−2i2i−2i2i0000−2−222−2−22200000000
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χ332222-2-2-2-2-222-222-2-2200000000222-2-2-2-2-2-2222-2-22−i2−i2i2i2i2i2−i2−i200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i20000000000000000000000002-2-220000−i2−i2i2i2i2i2−i2−i200000000
χ342222-2-2-2-2-222-222-2-2200000000222-2-2-2-2-2-2222-2-22−i2−i2i2i2i2i2−i2−i200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2000000000000000000000000-222-20000i2i2−i2−i2−i2−i2i2i200000000
χ352222-2-2-2-2-222-222-2-2200000000222-2-2-2-2-2-2222-2-22i2i2−i2−i2−i2−i2i2i200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i20000000000000000000000002-2-220000i2i2−i2−i2−i2−i2i2i200000000
χ362222-2-2-2-2-222-222-2-2200000000222-2-2-2-2-2-2222-2-22i2i2−i2−i2−i2−i2i2i200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2000000000000000000000000-222-20000−i2−i2i2i2i2i2−i2−i200000000
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χ4122-2-22-222-2222-2-2-2-2-1-2-22-2-2222-111-111-1-11-1-11-1110000000011-111-1-1-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i32i−2i2i−2i0000−i−iii−i−iii33−3−333−3−3000000000000000000000000
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χ4522-2-22-2-2-22-2-22222-2222-2-2-22-222-2-22-2-2-2-22-2-222220000000022-2-2-222-2000000000000000000000000000000000000000000000000000000002-2-220000
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χ4722-2-22-2-2-22-2-22222-22-2-2222-22-22-2-22-2-2-2-22-2-2222200000000-2-2222-2-2200000000000000002-2-22000022-2-2-2-22200000000000000000000000000000000
χ4822-2-22-2-2-22-2-22222-22-2-2222-22-22-2-22-2-2-2-22-2-2222200000000-2-2222-2-220000000000000000-222-20000-2-22222-2-200000000000000000000000000000000
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χ742-22-2-22-22-22-22-222-2-12-22-222-2-21-1111-11-11-11-1-1-112i−2i−2i2i−2i2i2i−2i-11-11-11-11−ii−iii−ii−ii−ii−i−ii−ii00000000−33−333−33−3−i3i3−i3i3i3−i3i3−i3000000000000000000000000
χ752-22-2-22-22-22-22-222-2-12-22-222-2-21-1111-11-11-11-1-1-11−2i2i2i−2i2i−2i−2i2i-11-11-11-11i−ii−i−ii−ii−ii−iii−ii−i000000003−33−3−33−33−i3i3−i3i3i3−i3i3−i3000000000000000000000000
χ762-22-2-22-22-22-22-222-2-12-22-222-2-21-1111-11-11-11-1-1-11−2i2i2i−2i2i−2i−2i2i-11-11-11-11i−ii−i−ii−ii−ii−iii−ii−i00000000−33−333−33−3i3−i3i3−i3−i3i3−i3i3000000000000000000000000
χ772-2-22-2-22-2-2-222-222222-2-22-222-2-2-22-22-22-2-2-22222-2000000002-2-22-2-2220000000000000000000000000000000000000000000000000000000000002-22-2
χ782-2-22-2-22-2-2-222-222222-2-22-222-2-2-22-22-22-2-2-22222-2000000002-2-22-2-222000000000000000000000000000000000000000000000000000000000000-22-22
χ792-2-22-2-22-2-2-222-22222-222-22-2-22-2-22-22-22-2-2-22222-200000000-222-222-2-2000000000000000000002-22-2000000002-2-222-2-22000000000000000000000000
χ802-2-22-2-22-2-2-222-22222-222-22-2-22-2-22-22-22-2-2-22222-200000000-222-222-2-200000000000000000000-22-2200000000-222-2-222-2000000000000000000000000
χ812-2-22-2-22-2-2-222-2222-1-222-22-2-2211-11-11-1111-1-1-1-11000000001-1-11-1-1113−3−33−333−33−3−33−333−300002-22-2−333−3−333−3-111-1-111-1000000000000000000000000
χ822-2-22-2-22-2-2-222-2222-1-222-22-2-2211-11-11-1111-1-1-1-11000000001-1-11-1-1113−3−33−333−33−3−33−333−30000-22-223−3−333−3−331-1-111-1-11000000000000000000000000
χ832-2-22-2-22-2-2-222-2222-1-222-22-2-2211-11-11-1111-1-1-1-11000000001-1-11-1-111−333−33−3−33−333−33−3−3300002-22-23−3−333−3−33-111-1-111-1000000000000000000000000
χ842-2-22-2-22-2-2-222-2222-1-222-22-2-2211-11-11-1111-1-1-1-11000000001-1-11-1-111−333−33−3−33−333−33−3−330000-22-22−333−3−333−31-1-111-1-11000000000000000000000000
χ852-2-22-2-2-2222-222-2-2222-2-2-22-222-2-22-22-2-2222-2-22-22000000002-2-2-222-220000000000000000000000000000000000000000000000000000000000002-2-22
χ862-2-22-2-2-2222-222-2-2222-2-2-22-222-2-22-22-2-2222-2-22-22000000002-2-2-222-22000000000000000000000000000000000000000000000000000000000000-222-2
χ872-2-22-2-2-2222-222-2-222-2222-22-2-2-2-22-22-2-2222-2-22-2200000000-2222-2-22-2000000000000000000002i−2i−2i2i000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ882-2-22-2-2-2222-222-2-222-2222-22-2-2-2-22-22-2-2222-2-22-2200000000-2222-2-22-200000000000000000000−2i2i2i−2i00000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ892-2-22-2-2-2222-222-2-22-1-2222-22-2-211-11-111-1-1-111-11-1000000001-1-1-111-113−3−33−333−3−333−33−3−3300002i−2i−2i2i−i3i3i3−i3i3−i3−i3i3−iii−ii−i−ii000000000000000000000000
χ902-2-22-2-2-2222-222-2-22-1-2222-22-2-211-11-111-1-1-111-11-1000000001-1-1-111-113−3−33−333−3−333−33−3−330000−2i2i2i−2ii3−i3−i3i3−i3i3i3−i3i−i−ii−iii−i000000000000000000000000
χ912-2-22-2-2-2222-222-2-22-1-2222-22-2-211-11-111-1-1-111-11-1000000001-1-1-111-11−333−33−3−333−3−33−333−300002i−2i−2i2ii3−i3−i3i3−i3i3i3−i3−iii−ii−i−ii000000000000000000000000
χ922-2-22-2-2-2222-222-2-22-1-2222-22-2-211-11-111-1-1-111-11-1000000001-1-1-111-11−333−33−3−333−3−33−333−30000−2i2i2i−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
χ94444444-4-4-4-4-44-4-4-44-2-4-4-4444-44-2-2-2-2-2-2222222-22200000000222-2-2-2-220000000000000000000000000000000000000000000000000000000000000000
χ954444-4-4444-4-4-4-4-44-4-200000000-2-2-2222-2-2-22222-22−2i2−2i22i22i2−2i2−2i22i22i200000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2000000000000000000000000000000000000000000000000
χ964444-4-4444-4-4-4-4-44-4-200000000-2-2-2222-2-2-22222-222i22i2−2i2−2i22i22i2−2i2−2i200000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2000000000000000000000000000000000000000000000000
χ974444-4-4-4-4-444-444-4-4-200000000-2-2-2222222-2-2-222-2−2i2−2i22i22i22i22i2−2i2−2i200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2000000000000000000000000000000000000000000000000
χ984444-4-4-4-4-444-444-4-4-200000000-2-2-2222222-2-2-222-22i22i2−2i2−2i2−2i2−2i22i22i200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2000000000000000000000000000000000000000000000000
χ9944-4-44-444-4444-4-4-4-4-244-444-4-4-4-222-222-2-22-2-22-22200000000-2-22-2-22220000000000000000000000000000000000000000000000000000000000000000
χ10044-4-44-4-4-44-4-44444-4-244-4-4-44-44-222-22222-222-2-2-2-200000000-2-2222-2-220000000000000000000000000000000000000000000000000000000000000000
χ10144-4-4-4444-4-4-4-444-444000000004-4-4-44444-4-4-44-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10244-4-4-4444-4-4-4-444-44-200000000-2222-2-2-2-2222-222-2000000000000000066−6−6−6−66666−6−6−6−666000000000000000000000000000000000000000000000000
χ10344-4-4-4444-4-4-4-444-44-200000000-2222-2-2-2-2222-222-20000000000000000−6−66666−6−6−6−66666−6−6000000000000000000000000000000000000000000000000
χ10444-4-4-44-4-4444-4-4-4444000000004-4-4-444-4-4444-4-44-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10544-4-4-44-4-4444-4-4-444-200000000-2222-2-222-2-2-222-22000000000000000066−6−6−6−666−6−66666−6−6000000000000000000000000000000000000000000000000
χ10644-4-4-44-4-4444-4-4-444-200000000-2222-2-222-2-2-222-220000000000000000−6−66666−6−666−6−6−6−666000000000000000000000000000000000000000000000000
χ1074-44-44-44-444-4-4-44-44-2000000002-22-2-22-22-2-22-222222−2222−2222−2222−2200000000−22−22−22−22−22−22−22−22000000000000000000000000000000000000000000000000
χ1084-44-44-44-444-4-4-44-44-2000000002-22-2-22-22-2-22-2222−2222−2222−2222−2222000000002−22−22−22−22−22−22−22−2000000000000000000000000000000000000000000000000
χ1094-44-44-4-44-4-44-44-444-2000000002-22-2-222-222-222-2-222−2222−22−2222−222200000000−22−22−22−222−22−22−22−2000000000000000000000000000000000000000000000000
χ1104-44-44-4-44-4-44-44-444-2000000002-22-2-222-222-222-2-2−2222−222222−2222−22000000002−22−22−22−2−22−22−22−22000000000000000000000000000000000000000000000000
χ1114-44-4-444-44-4444-4-4-4-2-44-4-4444-42-2222-2-22-22-22-22-2000000002-222-22-2-20000000000000000000000000000000000000000000000000000000000000000
χ1124-44-4-44-44-44-44-444-4-2-44-44-4-4442-2222-22-22-22-2-2-22000000002-22-22-22-20000000000000000000000000000000000000000000000000000000000000000
χ1134-4-44444-4-44-4-44-44-4400000000-4-444-444-4-44-4-4-44400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1144-4-44444-4-44-4-44-44-4-20000000022-2-22-2-222-2222-2-20000000000000000i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6000000000000000000000000000000000000000000000000
χ1154-4-44444-4-44-4-44-44-4-20000000022-2-22-2-222-2222-2-20000000000000000−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6000000000000000000000000000000000000000000000000
χ1164-4-4444-444-44-4-44-4-4400000000-4-444-44-444-444-4-4-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1174-4-4444-444-44-4-44-4-4-20000000022-2-22-22-2-22-2-22220000000000000000i6−i6−i6i6i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6000000000000000000000000000000000000000000000000
χ1184-4-4444-444-44-4-44-4-4-20000000022-2-22-22-2-22-2-22220000000000000000−i6i6i6−i6−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6000000000000000000000000000000000000000000000000
χ1194-4-44-4-44-4-4-444-4444-24-4-44-444-422-22-22-2222-2-2-2-2200000000-222-222-2-20000000000000000000000000000000000000000000000000000000000000000
χ1204-4-44-4-4-4444-444-4-44-24-4-4-44-44422-22-222-2-2-222-22-200000000-2222-2-22-20000000000000000000000000000000000000000000000000000000000000000

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