Finite Group Databasebeta

← Group #10742716

Character table — Group #10742716

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11111111111111112222222222222222444444444444444444444444444444444444444488888888888888888888881212121212121212242424242424242424242424
order1222222222222222366666666666666622222222444444446666666612121212121212121212121212121212444444666612121212121212121212121244444444224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11111-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1-1-111
χ911111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-1
χ1011111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111
χ1111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1
χ1211111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
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
χ182222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-222-1-1-1-1-1-1-1-11111111100000000000000000000
χ192222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111111111111100000000000000000000
χ202222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-211111111-1-1-1-1-1-1-1-100000000000000000000
χ212222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222222222-2-2-2-211111111-1-1-1-1-1-1-1-11111111122-2-2-2-2-1-1-1-11111-1-1-1-1111100000000000000000000
χ222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-2-222-2-2-1-1-1-111111111-1-1-1-100000000000000000000
χ232222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-2-222221111-1-1-1-11111-1-1-1-100000000000000000000
χ242222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-122-2-2221111-1-1-1-1-1-1-1-1111100000000000000000000
χ2522222-2-2-2-2-222-2-22-22222222-2-2-2-2-22-2-2-2000022-2-200002i2i−2i−2i00000000000000002i2i2i2i−2i−2i−2i−2i002i−2i0022-2-2000000002i2i−2i−2i00000000000000000000
χ2622222-2-2-2-2-222-2-22-22222222-2-2-2-2-22-2-2-2000022-2-20000−2i−2i2i2i0000000000000000−2i−2i−2i−2i2i2i2i2i00−2i2i0022-2-200000000−2i−2i2i2i00000000000000000000
χ2722222-2-2-2-2-222-2-22-22222222-2-2-2-2-22-2-2-20000-2-22200002i2i−2i−2i00000000000000002i2i2i2i−2i−2i−2i−2i00−2i2i00-2-22200000000−2i−2i2i2i00000000000000000000
χ2822222-2-2-2-2-222-2-22-22222222-2-2-2-2-22-2-2-20000-2-2220000−2i−2i2i2i0000000000000000−2i−2i−2i−2i2i2i2i2i002i−2i00-2-222000000002i2i−2i−2i00000000000000000000
χ2922222-2-2-2-2-222-2-22-2-1-1-1-1-1-1-111111-1111000022-2-200002i2i−2i−2i−i3−i3−i3−i3i3i3i3i33333−3−3−3−3−i−i−i−iiiii002i−2i00-1-111−i3−i3i3i333−3−3−i−iii00000000000000000000
χ3022222-2-2-2-2-222-2-22-2-1-1-1-1-1-1-111111-1111000022-2-200002i2i−2i−2ii3i3i3i3−i3−i3−i3−i3−3−3−3−33333−i−i−i−iiiii002i−2i00-1-111i3i3−i3−i3−3−333−i−iii00000000000000000000
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χ3422222-2-2-2-2-222-2-22-2-1-1-1-1-1-1-111111-11110000-2-22200002i2i−2i−2ii3i3i3i3−i3−i3−i3−i3−3−3−3−33333−i−i−i−iiiii00−2i2i0011-1-1−i3−i3i3i333−3−3ii−i−i00000000000000000000
χ3522222-2-2-2-2-222-2-22-2-1-1-1-1-1-1-111111-11110000-2-2220000−2i−2i2i2i−i3−i3−i3−i3i3i3i3i3−3−3−3−33333iiii−i−i−i−i002i−2i0011-1-1i3i3−i3−i333−3−3−i−iii00000000000000000000
χ3622222-2-2-2-2-222-2-22-2-1-1-1-1-1-1-111111-11110000-2-2220000−2i−2i2i2ii3i3i3i3−i3−i3−i3−i33333−3−3−3−3iiii−i−i−i−i002i−2i0011-1-1−i3−i3i3i3−3−333−i−iii00000000000000000000
χ37222-2-222-2-2-2-2-2222-2222-2-2-2-22222-22-2-2-200002-22-22i2i−2i−2i0000000000002i2i−2i−2i2i2i−2i−2i000000002i−2i00002-22-200002i−2i2i−2i000000000000000000000000
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χ43222-2-222-2-2-2-2-2222-2-1-1-11111-1-1-1-11-111100002-22-2−2i−2i2i2i0000−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i−3−333−3−333−2i2i0000-11-11−i3i3−i3i3i−ii−i−33−3300000000000000000000
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χ46222-2-222-2-2-2-2-2222-2-1-1-11111-1-1-1-11-11110000-22-222i2i−2i−2i0000i3i3−i3−i3i3i3−i3−i3−i−iii−i−iii−3−333−3−333−2i2i00001-11-1−i3i3−i3i3i−ii−i3−33−300000000000000000000
χ47222-2-222-2-2-2-2-2222-2-1-1-11111-1-1-1-11-11110000-22-22−2i−2i2i2i0000−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i−3−333−3−3332i−2i00001-11-1i3−i3i3−i3−ii−ii3−33−300000000000000000000
χ48222-2-222-2-2-2-2-2222-2-1-1-11111-1-1-1-11-11110000-22-22−2i−2i2i2i0000i3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i33−3−333−3−32i−2i00001-11-1−i3i3−i3i3−ii−ii−33−3300000000000000000000
χ49222-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2-2-22222222-2-22-2-220000000022-2-2-2-222000000000000000000002-22-2-222-2-220000000000000000000000000000
χ50222-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2-2-22222222-2-2-222-20000000022-2-2-2-22200000000000000000000-22-222-2-222-20000000000000000000000000000
χ51222-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2-2-222222-2-2222-2-2200000000-2-22222-2-200000000000000000000-222-2-22-222-20000000000000000000000000000
χ52222-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2-2-222222-2-222-222-200000000-2-22222-2-2000000000000000000002-2-222-22-2-220000000000000000000000000000
χ53222-2-2-2-2222-2-2-2-222-1-1-111111111-1-1-1-1-122-2-22-2-2200000000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300002-2-111-1-111-1−i3i3i3−i3−i3i3i3−i300000000000000000000
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χ56222-2-2-2-2222-2-2-2-222-1-1-111111111-1-1-1-1-122-2-2-222-200000000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000-221-1-111-1-11−i3i3i3−i3−i3i3i3−i300000000000000000000
χ57222-2-2-2-2222-2-2-2-222-1-1-111111111-1-1-1-1-1-2-2222-2-220000000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000-22-111-11-1-11−i3i3i3−i3i3−i3−i3i300000000000000000000
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χ6122-22-2-2-222-22-222-2-222-222-2-222-2-22-22-2-2000000002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000002i2i−2i−2i0000002-20000
χ6222-22-2-2-222-22-222-2-222-222-2-222-2-22-22-2-2000000002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000−2i−2i2i2i000000-220000
χ6322-22-2-2-222-22-222-2-222-222-2-222-2-22-22-2-200000000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000002i2i−2i−2i000000-220000
χ6422-22-2-2-222-22-222-2-222-222-2-222-2-22-22-2-200000000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000−2i−2i2i2i0000002-20000
χ6522-2-22-2-2-2-22-2222-2222-2-2-22222-2-2-2-2-222000000002-2-220000000000002-2-222-2-2200000000000000000000000000000022-2-20000002-200000000
χ6622-2-22-2-2-2-22-2222-2222-2-2-22222-2-2-2-2-222000000002-2-220000000000002-2-222-2-22000000000000000000000000000000-2-222000000-2200000000
χ6722-2-22-2-2-2-22-2222-2222-2-2-22222-2-2-2-2-22200000000-222-2000000000000-222-2-222-200000000000000000000000000000022-2-2000000-2200000000
χ6822-2-22-2-2-2-22-2222-2222-2-2-22222-2-2-2-2-22200000000-222-2000000000000-222-2-222-2000000000000000000000000000000-2-2220000002-200000000
χ692-22-2-22-22-22222-2-2-22-222-22-22-22-22-2-22-20000000000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000002i−2i2i−2i000000002-200
χ702-22-2-22-22-22222-2-2-22-222-22-22-22-22-2-22-20000000000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000−2i2i−2i2i00000000-2200
χ712-22-2-22-22-22222-2-2-22-222-22-22-22-22-2-22-2000000000000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000002i−2i2i−2i00000000-2200
χ722-22-2-22-22-22222-2-2-22-222-22-22-22-22-2-22-2000000000000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000−2i2i−2i2i000000002-200
χ732-22-2-2-22-22-222-22-222-222-22-2-22-22-2-22-220000000000002-2-2200000000000000002-22-2-22-2200000000000000000000002-22-2000000002-2000000
χ742-22-2-2-22-22-222-22-222-222-22-2-22-22-2-22-220000000000002-2-2200000000000000002-22-2-22-220000000000000000000000-22-2200000000-22000000
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χ812-2-2-22-222-2-22-22-2222-2-22-2-222-2-2222-2-222-2-220000000000002-2-22-222-20000000000000000000000000000000000000000002-2-2200000000002-2
χ822-2-2-22-222-2-22-22-2222-2-22-2-222-2-2222-2-222-2-220000000000002-2-22-222-2000000000000000000000000000000000000000000-222-20000000000-22
χ832-2-2-22-222-2-22-22-2222-2-22-2-222-2-2222-2-22-222-2000000000000-222-22-2-220000000000000000000000000000000000000000002-2-220000000000-22
χ842-2-2-22-222-2-22-22-2222-2-22-2-222-2-2222-2-22-222-2000000000000-222-22-2-22000000000000000000000000000000000000000000-222-200000000002-2
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χ8844-44-4-4-444-44-444-4-4-2-22-2-222-2-222-22-222000000004i−4i4i−4i000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ8944-44-4-4-444-44-444-4-4-2-22-2-222-2-222-22-22200000000−4i4i−4i4i0000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000000000
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χ994-4444-444-44-4-4-44-4-4-22-22-22-22-22-2-222-220000000000000000000000000000000023−23−2323−232323−23000000000000000000000000000000000000000000
χ1004-4444-444-44-4-4-44-4-4-22-22-22-22-22-2-222-2200000000000000000000000000000000−232323−2323−23−2323000000000000000000000000000000000000000000
χ1014-44-4-44-44-44444-4-4-4-22-2-22-22-22-22-222-220000000000004i−4i4i−4i0000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000
χ1024-44-4-44-44-44444-4-4-4-22-2-22-22-22-22-222-22000000000000−4i4i−4i4i00000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000
χ1034-44-4-4-44-44-444-44-44-22-2-22-222-22-222-22-20000000000004-4-440000000000000000-22-222-22-2000000000000000000000000000000000000000000
χ1044-44-4-4-44-44-444-44-44-22-2-22-222-22-222-22-2000000000000-444-400000000000000002-22-2-22-22000000000000000000000000000000000000000000
χ1054-4-44-44-44-4-4-44-4444-2222-2-222-2-22-2-222-24-44-4000000000000-22-22-22-220000000000000000000000000000000000000000000000000000000000
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χ1084-4-44-4-44-444-444-44-4-2222-2-22-222-22-2-2-220000000000000000−2i32i3−2i32i32i3−2i32i3−2i30000000000000000000000000000000000000000000000000000000000
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χ1104-4-4-444-4-4444-4-444-44-4-44-4-44-444-4-4444-40000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1114-4-4-444-4-4444-4-444-4-222-222-22-2-222-2-2-220000000000000000−2i32i32i3−2i3−2i32i32i3−2i30000000000000000000000000000000000000000000000000000000000
χ1124-4-4-444-4-4444-4-444-4-222-222-22-2-222-2-2-2200000000000000002i3−2i3−2i32i32i3−2i3−2i32i30000000000000000000000000000000000000000000000000000000000
χ1134-4-4-44-444-4-44-44-444-222-222-2-222-2-2-222-24-4-44000000000000-222-22-2-220000000000000000000000000000000000000000000000000000000000
χ1144-4-4-44-444-4-44-44-444-222-222-2-222-2-2-222-2-444-40000000000002-2-22-222-20000000000000000000000000000000000000000000000000000000000

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