Finite Group Databasebeta

← Group #10701749

Character table — Group #10701749

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order122222222222222222223666666666666666444444446666666612121212121212121212121212121212222244446666666612121212121212124444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1822222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ1922222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ2022222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-222-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ23222222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ24222222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ2522222222-2-2-2-222-2-222-2-2222222-2-2-2-2-2-2-2-22222-2-222-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ2622222222-2-2-2-222-2-222-2-2222222-2-2-2-2-2-2-2-222-2-222-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ2722222222-2-2-2-222-2-222-2-2-1-1-1-1-1-111111111-1-122-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ2822222222-2-2-2-222-2-222-2-2-1-1-1-1-1-111111111-1-122-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ2922222222-2-2-2-222-2-222-2-2-1-1-1-1-1-111111111-1-1-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
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χ3122222222-2-2-2-2-2-222-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ3222222222-2-2-2-2-2-222-2-222222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ3322222222-2-2-2-2-2-222-2-222-1-1-1-1-1-111111111-1-122-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
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χ3622222222-2-2-2-2-2-222-2-222-1-1-1-1-1-111111111-1-1-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
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χ38222-2-2-22-222-2-2222-2-2-22-2222-2-2-22222-2-2-2-22-20000000022-2-222-2-20000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ39222-2-2-22-222-2-2-2-2-2222-22222-2-2-22222-2-2-2-22-200000000-2-222-2-22200000000000000000000000000000000000000000000000000002-2-22
χ40222-2-2-22-222-2-2-2-2-2222-22222-2-2-22222-2-2-2-22-200000000-2-222-2-2220000000000000000000000000000000000000000000000000000-222-2
χ41222-2-2-22-2-2-22222-22-2-2-22222-2-2-2-2-2-2-222222-20000000022-2-2-2-2220000000000000000000000000000000000000000000000002i−2i2i−2i0000
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χ652-2-2-2-2222-222-22-2-22-222-22-2-2-2-22-2-22222-2-222000000002-2-22-222-20000000000000000002-2002-200002-2-2200002-2-220000000000000000
χ662-2-2-2-2222-222-22-2-22-222-22-2-2-2-22-2-22222-2-222000000002-2-22-222-2000000000000000000-2200-220000-222-20000-222-20000000000000000
χ672-2-2-2-2222-222-22-2-22-222-2-11111-111-1-1-1-111-1-100000000-111-11-1-11−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3002-2002-2−i3i3i3−i3-111-1−i3i3i3−i3-111-10000000000000000
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χ8744-4-44-4-4400000000000044-4-44-400000000-444-4000000000000004-44-40000000000000000000000000000000000000000000000000000
χ8844-4-44-4-4400000000000044-4-44-400000000-44-4400000000000000-44-440000000000000000000000000000000000000000000000000000
χ8944-4-44-4-44000000000000-2-222-22−2i32i3−2i32i32i3−2i32i3−2i32-24-400000000000000-22-22−2i32i3−2i32i3000000000000000000000000000000000000000000000000
χ9044-4-44-4-44000000000000-2-222-22−2i32i3−2i32i32i3−2i32i3−2i32-2-44000000000000002-22-22i3−2i32i3−2i3000000000000000000000000000000000000000000000000
χ9144-4-44-4-44000000000000-2-222-222i3−2i32i3−2i3−2i32i3−2i32i32-24-400000000000000-22-222i3−2i32i3−2i3000000000000000000000000000000000000000000000000
χ9244-4-44-4-44000000000000-2-222-222i3−2i32i3−2i3−2i32i3−2i32i32-2-44000000000000002-22-2−2i32i3−2i32i3000000000000000000000000000000000000000000000000
χ934-444-4-4-440000000000004-444-4-400000000-44004-400000000000000004-4-44000000000000000000000000000000000000000000000000
χ944-444-4-4-440000000000004-444-4-400000000-4400-440000000000000000-444-4000000000000000000000000000000000000000000000000
χ954-444-4-4-44000000000000-22-2-222−2i32i32i3−2i3−2i32i32i3−2i32-2004-4000000000000−2i32i32i3−2i3-222-2000000000000000000000000000000000000000000000000
χ964-444-4-4-44000000000000-22-2-222−2i32i32i3−2i3−2i32i32i3−2i32-200-440000000000002i3−2i3−2i32i32-2-22000000000000000000000000000000000000000000000000
χ974-444-4-4-44000000000000-22-2-2222i3−2i3−2i32i32i3−2i3−2i32i32-2004-40000000000002i3−2i3−2i32i3-222-2000000000000000000000000000000000000000000000000
χ984-444-4-4-44000000000000-22-2-2222i3−2i3−2i32i32i3−2i3−2i32i32-200-44000000000000−2i32i32i3−2i32-2-22000000000000000000000000000000000000000000000000
χ994-44-444-4-40000000000004-44-44400000000-4-400004i−4i0000000000000000004i−4i−4i4i00000000000000000000000000000000000000000000
χ1004-44-444-4-40000000000004-44-44400000000-4-40000−4i4i000000000000000000−4i4i4i−4i00000000000000000000000000000000000000000000
χ1014-44-444-4-4000000000000-22-22-2-2−2i32i32i3−2i32i3−2i3−2i32i32200004i−4i000000000000000000−2i2i2i−2i23−23−23230000000000000000000000000000000000000000
χ1024-44-444-4-4000000000000-22-22-2-2−2i32i32i3−2i32i3−2i3−2i32i3220000−4i4i0000000000000000002i−2i−2i2i−232323−230000000000000000000000000000000000000000
χ1034-44-444-4-4000000000000-22-22-2-22i3−2i3−2i32i3−2i32i32i3−2i32200004i−4i000000000000000000−2i2i2i−2i−232323−230000000000000000000000000000000000000000
χ1044-44-444-4-4000000000000-22-22-2-22i3−2i3−2i32i3−2i32i32i3−2i3220000−4i4i0000000000000000002i−2i−2i2i23−23−23230000000000000000000000000000000000000000
χ1054-4-444-44-44-44-44-4444-4-4-4-222-2-22-2-222-2-222-2200000000-22-22-22-2200000000000000000000000000000000000000000000000000000000
χ1064-4-444-44-44-44-4-44-4-4-4444-222-2-22-2-222-2-222-22000000002-22-22-22-200000000000000000000000000000000000000000000000000000000
χ1074-4-444-44-4-44-444-4-4-44-444-222-2-2222-2-222-2-2-2200000000-22-222-22-200000000000000000000000000000000000000000000000000000000
χ1084-4-444-44-4-44-44-4444-44-4-4-222-2-2222-2-222-2-2-22000000002-22-2-22-2200000000000000000000000000000000000000000000000000000000

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