Finite Group Databasebeta

← Group #10740367

Character table — Group #10740367

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11111111111111112222222222222222444444444444444444444444444444444444444488888888888888888888881212121212121212242424242424242424242424
order1222222222222222366666666666666644444444444444441212121212121212121212121212121212121212121212124444441212121212121212121212121212121244444444222244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-111-1-1-1-1
χ911111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111
χ1011111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ1111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1
χ1211111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-111-1-1
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ172222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ182222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111111111111100000000000000000000
χ192222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000000000
χ202222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2222211111111-1-1-1-1-1-1-1-100000000000000000000
χ212222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222222222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-2-2-2-222-1-1-1-111111111-1-1-1-100000000000000000000
χ222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-2-2-2-211111111-1-1-1-1-1-1-1-1111111112222-2-21111-1-1-1-1-1-1-1-1111100000000000000000000
χ232222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2222222221111111111111111-1-1-1-1-1-1-1-1-2-222-2-2-1-1-1-11111-1-1-1-1111100000000000000000000
χ242222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-122-2-2221111-1-1-1-11111-1-1-1-100000000000000000000
χ2522222-22-2-2-22-2-2-2-22222222-2-2-2-22-2-2-2-2200002i2i−2i−2i2i2i−2i−2i0000000000002i2i2i2i−2i−2i−2i−2i0000000000002-22i2i−2i−2i0000000022-2-200000000000000000000
χ2622222-22-2-2-22-2-2-2-22222222-2-2-2-22-2-2-2-2200002i2i−2i−2i−2i−2i2i2i0000000000002i2i2i2i−2i−2i−2i−2i000000000000-22−2i−2i2i2i00000000-2-22200000000000000000000
χ2722222-22-2-2-22-2-2-2-22222222-2-2-2-22-2-2-2-220000−2i−2i2i2i2i2i−2i−2i000000000000−2i−2i−2i−2i2i2i2i2i000000000000-222i2i−2i−2i00000000-2-22200000000000000000000
χ2822222-22-2-2-22-2-2-2-22222222-2-2-2-22-2-2-2-220000−2i−2i2i2i−2i−2i2i2i000000000000−2i−2i−2i−2i2i2i2i2i0000000000002-2−2i−2i2i2i0000000022-2-200000000000000000000
χ2922222-22-2-2-22-2-2-2-22-1-1-1-1-1-11111-11111-100002i2i−2i−2i2i2i−2i−2i00003333−3−3−3−3−i−i−i−iiiii−i3−i3−i3−i3i3i3i3i300002-2−i−iii−i3−i3i3i333−3−3-1-11100000000000000000000
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χ3422222-22-2-2-22-2-2-2-22-1-1-1-1-1-11111-11111-10000−2i−2i2i2i2i2i−2i−2i0000−3−3−3−33333iiii−i−i−i−i−i3−i3−i3−i3i3i3i3i30000-22−i−iiii3i3−i3−i333−3−311-1-100000000000000000000
χ3522222-22-2-2-22-2-2-2-22-1-1-1-1-1-11111-11111-10000−2i−2i2i2i−2i−2i2i2i00003333−3−3−3−3iiii−i−i−i−ii3i3i3i3−i3−i3−i3−i300002-2ii−i−ii3i3−i3−i333−3−3-1-11100000000000000000000
χ3622222-22-2-2-22-2-2-2-22-1-1-1-1-1-11111-11111-10000−2i−2i2i2i−2i−2i2i2i0000−3−3−3−33333iiii−i−i−i−i−i3−i3−i3−i3i3i3i3i300002-2ii−i−i−i3−i3i3i3−3−333-1-11100000000000000000000
χ372222-2-2-222-2-22-2-22-22222-2-22-2-2-2-2222-2-22i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000002i2i−2i−2i000000002-2000000
χ382222-2-2-222-2-22-2-22-22222-2-22-2-2-2-2222-2-22i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000−2i−2i2i2i00000000-22000000
χ392222-2-2-222-2-22-2-22-22222-2-22-2-2-2-2222-2-2−2i−2i2i2i000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000002i2i−2i−2i00000000-22000000
χ402222-2-2-222-2-22-2-22-22222-2-22-2-2-2-2222-2-2−2i−2i2i2i000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000−2i−2i2i2i000000002-2000000
χ4122-2-22222-2-2-2-22-22-222-2-22-2-222-2222-2-2-22i−2i2i−2i00002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i00000000000000002-200002i−2i2i−2i2-22-20000000000000000000000000000
χ4222-2-22222-2-2-2-22-22-222-2-22-2-222-2222-2-2-22i−2i2i−2i0000−2i2i−2i2i00002i−2i2i−2i2i−2i2i−2i0000000000000000-220000−2i2i−2i2i-22-220000000000000000000000000000
χ4322-2-22222-2-2-2-22-22-222-2-22-2-222-2222-2-2-2−2i2i−2i2i00002i−2i2i−2i0000−2i2i−2i2i−2i2i−2i2i0000000000000000-2200002i−2i2i−2i-22-220000000000000000000000000000
χ4422-2-22222-2-2-2-22-22-222-2-22-2-222-2222-2-2-2−2i2i−2i2i0000−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i00000000000000002-20000−2i2i−2i2i2-22-20000000000000000000000000000
χ4522-2-22222-2-2-2-22-22-2-1-111-111-1-11-1-1-11112i−2i2i−2i00002i−2i2i−2i0000−ii−ii−ii−ii−i3−i3i3i3−i3−i3i3i333−3−333−3−32-20000−ii−ii-11-11−i3i3−i3i33−33−300000000000000000000
χ4622-2-22222-2-2-2-22-22-2-1-111-111-1-11-1-1-11112i−2i2i−2i00002i−2i2i−2i0000−ii−ii−ii−iii3i3−i3−i3i3i3−i3−i3−3−333−3−3332-20000−ii−ii-11-11i3−i3i3−i3−33−3300000000000000000000
χ4722-2-22222-2-2-2-22-22-2-1-111-111-1-11-1-1-11112i−2i2i−2i0000−2i2i−2i2i0000−ii−ii−ii−ii−i3−i3i3i3−i3−i3i3i333−3−333−3−3-220000i−ii−i1-11-1i3−i3i3−i3−33−3300000000000000000000
χ4822-2-22222-2-2-2-22-22-2-1-111-111-1-11-1-1-11112i−2i2i−2i0000−2i2i−2i2i0000−ii−ii−ii−iii3i3−i3−i3i3i3−i3−i3−3−333−3−333-220000i−ii−i1-11-1−i3i3−i3i33−33−300000000000000000000
χ4922-2-22222-2-2-2-22-22-2-1-111-111-1-11-1-1-1111−2i2i−2i2i00002i−2i2i−2i0000i−ii−ii−ii−i−i3−i3i3i3−i3−i3i3i3−3−333−3−333-220000−ii−ii1-11-1i3−i3i3−i33−33−300000000000000000000
χ5022-2-22222-2-2-2-22-22-2-1-111-111-1-11-1-1-1111−2i2i−2i2i00002i−2i2i−2i0000i−ii−ii−ii−ii3i3−i3−i3i3i3−i3−i333−3−333−3−3-220000−ii−ii1-11-1−i3i3−i3i3−33−3300000000000000000000
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χ5222-2-22222-2-2-2-22-22-2-1-111-111-1-11-1-1-1111−2i2i−2i2i0000−2i2i−2i2i0000i−ii−ii−ii−ii3i3−i3−i3i3i3−i3−i333−3−333−3−32-20000i−ii−i-11-11i3−i3i3−i33−33−300000000000000000000
χ5322-2-22-22-222-22-22-2-222-2-22-22-2-222-2-222-2000000002-2-222i2i−2i−2i00000000000000002i2i−2i−2i−2i−2i2i2i002i−2i002-2-220000−2i2i2i−2i000000000000000000000000
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χ6322-2-22-22-222-22-22-2-2-1-111-11-111-1-111-1-1100000000-222-2−2i−2i2i2i−i3i3−i3i3i3−i3i3−i333−3−3−3−333ii−i−i−i−iii002i−2i001-1-11i3−i3−i3i3i−i−ii3−3−3300000000000000000000
χ6422-2-22-22-222-22-22-2-2-1-111-11-111-1-111-1-1100000000-222-2−2i−2i2i2ii3−i3i3−i3−i3i3−i3i3−3−33333−3−3ii−i−i−i−iii002i−2i001-1-11−i3i3i3−i3i−i−ii−333−300000000000000000000
χ6522-2-2-2-2-22-222-2-222222-2-2-22-2-2-22-222-2222-2-220000000000002-2-222-2-2200000000000000000000000000000000000000000022-2-2002-200000000
χ6622-2-2-2-2-22-222-2-222222-2-2-22-2-2-22-222-2222-2-220000000000002-2-222-2-22000000000000000000000000000000000000000000-2-22200-2200000000
χ6722-2-2-2-2-22-222-2-222222-2-2-22-2-2-22-222-222-222-2000000000000-222-2-222-200000000000000000000000000000000000000000022-2-200-2200000000
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χ692-22-222-2-2222-2-2-22-22-22-222-22-2-2-22-222-200002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000002i−2i2i−2i00000000002-20000
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χ722-22-222-2-2222-2-2-22-22-22-222-22-2-2-22-222-20000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000−2i2i−2i2i00000000002-20000
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χ752-22-22-2-22-2-22222-2-22-22-2222-222-2-22-2-2-20000-222-20000000000000000-22-222-22-200000000000000000000000000000000002i−2i2i−2i0000000000−2i2i
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χ812-2-22-22222-22-2-22-2-22-2-22-22-22-222-222-2-20000000000002i−2i−2i2i00000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000002i−2i−2i2i000000002-200
χ822-2-22-22222-22-2-22-2-22-2-22-22-22-222-222-2-20000000000002i−2i−2i2i00000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000−2i2i2i−2i00000000-2200
χ832-2-22-22222-22-2-22-2-22-2-22-22-22-222-222-2-2000000000000−2i2i2i−2i0000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000002i−2i−2i2i00000000-2200
χ842-2-22-22222-22-2-22-2-22-2-22-22-22-222-222-2-2000000000000−2i2i2i−2i0000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000−2i2i2i−2i000000002-200
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χ864444-44-4-4-44-4-444-4-4-2-2-2-2222-2-2-22222-220000000000000000−2i3−2i32i32i32i32i3−2i3−2i30000000000000000000000000000000000000000000000000000000000
χ874444-44-4-4-44-4-444-4-4-2-2-2-2222-2-2-22222-2200000000000000002i32i3−2i3−2i3−2i3−2i32i32i30000000000000000000000000000000000000000000000000000000000
χ884444-4-4-444-4-44-4-44-4-2-2-2-222-22222-2-2-2224i4i−4i−4i000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000000000
χ894444-4-4-444-4-44-4-44-4-2-2-2-222-22222-2-2-222−4i−4i4i4i0000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000000000
χ9044-4-4-44-4-44-4444-4-4444-4-4-44444-4-4-4-44-440000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9144-4-4-44-4-44-4444-4-44-2-2222-2-2-2-22222-22-2000000000000000023−23−2323−232323−230000000000000000000000000000000000000000000000000000000000
χ9244-4-4-44-4-44-4444-4-44-2-2222-2-2-2-22222-22-20000000000000000−232323−2323−23−23230000000000000000000000000000000000000000000000000000000000
χ9344-4-4-4-4-44-444-4-4444-2-2222-2222-22-2-22-2-24-4-44000000000000-222-2-222-20000000000000000000000000000000000000000000000000000000000
χ9444-4-4-4-4-44-444-4-4444-2-2222-2222-22-2-22-2-2-444-40000000000002-2-222-2-220000000000000000000000000000000000000000000000000000000000
χ954-44-444-4-4444-4-4-44-4-22-22-2-22-2222-22-2-2200004i−4i4i−4i0000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ964-44-444-4-4444-4-4-44-4-22-22-2-22-2222-22-2-220000−4i4i−4i4i00000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000000000
χ974-44-44-4-44-4-44444-4-4-22-22-2-2-22-2-222-222200004-4-440000000000000000-22-222-22-200000000000000000000000000000000000000000000000000
χ984-44-44-4-44-4-44444-4-4-22-22-2-2-22-2-222-22220000-444-400000000000000002-22-2-22-2200000000000000000000000000000000000000000000000000
χ994-44-4-4444-44-44-4-4-444-44-4-4-444-4-44-44-4440000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1004-44-4-4444-44-44-4-4-44-22-2222-2-222-22-22-2-200000000000000000000000000000000−2i32i3−2i32i32i3−2i32i3−2i3000000000000000000000000000000000000000000
χ1014-44-4-4444-44-44-4-4-44-22-2222-2-222-22-22-2-2000000000000000000000000000000002i3−2i32i3−2i3−2i32i3−2i32i3000000000000000000000000000000000000000000
χ1024-44-4-4-44-44-4-4-44444-22-222222-2-2-2-22-22-20000000000004-44-40000000000000000-22-22-22-22000000000000000000000000000000000000000000
χ1034-44-4-4-44-44-4-4-44444-22-222222-2-2-2-22-22-2000000000000-44-4400000000000000002-22-22-22-2000000000000000000000000000000000000000000
χ1044-4-4444-4-4-4-4-44-44444-4-444-444-44-44-4-4-440000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1054-4-4444-4-4-4-4-44-4444-222-2-22-2-22-22-2222-200000000000000000000000023−23−232323−23−232300000000000000000000000000000000000000000000000000
χ1064-4-4444-4-4-4-4-44-4444-222-2-22-2-22-22-2222-2000000000000000000000000−232323−23−232323−2300000000000000000000000000000000000000000000000000
χ1074-4-444-4-4444-4-44-4-444-4-444-4-4-44-4-4-444440000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1084-4-444-4-4444-4-44-4-44-222-2-2222-2222-2-2-2-2000000000000000000000000−2i32i32i3−2i32i3−2i3−2i32i300000000000000000000000000000000000000000000000000
χ1094-4-444-4-4444-4-44-4-44-222-2-2222-2222-2-2-2-20000000000000000000000002i3−2i3−2i32i3−2i32i32i3−2i300000000000000000000000000000000000000000000000000
χ1104-4-44-44444-44-4-44-4-4-222-22-22-22-2-22-2-2220000000000004i−4i−4i4i0000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000000000
χ1114-4-44-44444-44-4-44-4-4-222-22-22-22-2-22-2-222000000000000−4i4i4i−4i00000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000000000
χ1124-4-44-4-44-4-44444-44-44-4-44-444-44-444-4-44-40000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1134-4-44-4-44-4-44444-44-4-222-22-2-22-22-2-222-220000000000000000000000000000000023−23−232323−23−2323000000000000000000000000000000000000000000
χ1144-4-44-4-44-4-44444-44-4-222-22-2-22-22-2-222-2200000000000000000000000000000000−232323−23−232323−23000000000000000000000000000000000000000000

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