Finite Group Databasebeta

← Group #10896512

Character table — Group #10896512

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order122222223444444444444666666612121212121212124444444412121212121212121212121212121212121212121212121244444444121212121212121212121212121212124444444488888888
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
χ5111111111111111-1-1-1-111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111-1-1-1-111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111-1-1-1-111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111-1-1-1-111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1211111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1311111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1411111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1511111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ17222222222-2-222222222-2-222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ18222222222-2-22222-2-2-2-2-2-2222222222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ19222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ2122222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ2322222222-1222222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-1-1-1-1-1-1-1-1111111111111111122-2-222-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2422222222-1222222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-1-1-1-1-1-1-1-11111111111111111-2-222-2-22211111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-122-2-2-2-2222222-1-1-1-1-1-1-111111111-2-222-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111122-2-2-2-222-1-1-1-11111-1-1-1-111110000000000000000
χ2622222222-122-2-2-2-2222222-1-1-1-1-1-1-111111111-2-222-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-11111-2-22222-2-21111-1-1-1-11111-1-1-1-10000000000000000
χ2722222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-11111111122-2-2-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-12222-2-2-2-2-1-1-1-111111111-1-1-1-10000000000000000
χ2822222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-11111111122-2-2-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-1-2-2-2-222221111-1-1-1-1-1-1-1-111110000000000000000
χ2922222222-1-2-222222222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ3022222222-1-2-222222222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
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χ3222222222-1-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2221111111111111111-1-1-1-1-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ3322222222-1-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-111111111-2-2-2-222221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
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χ3522222222-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111222222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111222222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
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χ402222-2-2-2-220022-2-2-2-22200222-2-2-2-22222-2-2-2-2-2200000000000000-2-222-2-2220000000000000000000000000000000000000000−22−222−22−2
χ412222-2-2-2-2200-2-22222-2-200222-2-2-2-2-2-2-2-22222-220000000000000022-2-2-2-22200000000000000000000000000000000000000002−2−222−2−22
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χ8544-4-4-44-444004-4-440000004-4-4-4-44444-4-4-4-444000000000000000000000000000000000000000000000000000000000000000000000000
χ8644-4-4-44-44400-444-40000004-4-4-4-444-4-44444-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ8744-4-4-44-44-2004-4-44000000-22222-2-2-2-22222-2-2000000000000000000000000−2i32i3−2i32i3−2i32i3−2i32i30000000000000000000000000000000000000000
χ8844-4-4-44-44-2004-4-44000000-22222-2-2-2-22222-2-20000000000000000000000002i3−2i32i3−2i32i3−2i32i3−2i30000000000000000000000000000000000000000
χ8944-4-4-44-44-200-444-4000000-22222-2-222-2-2-2-222000000000000000000000000−2i32i3−2i32i32i3−2i32i3−2i30000000000000000000000000000000000000000
χ9044-4-4-44-44-200-444-4000000-22222-2-222-2-2-2-2220000000000000000000000002i3−2i32i3−2i3−2i32i3−2i32i30000000000000000000000000000000000000000
χ914-44-4-444-440000004i−4i−4i4i00-44-4-44-440000000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ924-44-4-444-44000000−4i4i4i−4i00-44-4-44-44000000000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ934-44-4-444-4-20000004i−4i−4i4i002-222-22-223−2323−23−2323−23230000000000000000−2i2i2i−2i−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ944-44-4-444-4-20000004i−4i−4i4i002-222-22-2−2323−232323−2323−230000000000000000−2i2i2i−2i2i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ954-44-4-444-4-2000000−4i4i4i−4i002-222-22-223−2323−23−2323−232300000000000000002i−2i−2i2i2i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ964-44-4-444-4-2000000−4i4i4i−4i002-222-22-2−2323−232323−2323−2300000000000000002i−2i−2i2i−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ974-4-4444-4-444-400000000-44-4-444-4-4400000000000000004-4-44000000000000000000000000000000000000000000000000000000000000
χ984-4-4444-4-44-44000000004-4-4-444-4-440000000000000000-444-4000000000000000000000000000000000000000000000000000000000000
χ994-4-4444-4-4-24-400000000-4422-2-222-223−23−232323−23−232300000000-222-223−23−232300000000000000000000000000000000000000000000000000000000
χ1004-4-4444-4-4-24-400000000-4422-2-222-2−232323−23−232323−2300000000-222-2−232323−2300000000000000000000000000000000000000000000000000000000
χ1014-4-4444-4-4-2-44000000004-422-2-222-223−23−232323−23−2323000000002-2-22−232323−2300000000000000000000000000000000000000000000000000000000
χ1024-4-4444-4-4-2-44000000004-422-2-222-2−232323−23−232323−23000000002-2-2223−23−232300000000000000000000000000000000000000000000000000000000
χ1034-4-44-4-4444000000000000-4-44-444-4000000000000004-4000000000000000000004-4-440000000000000000000000000000000000000000
χ1044-4-44-4-4444000000000000-4-44-444-400000000000000-4400000000000000000000-444-40000000000000000000000000000000000000000
χ1054-4-44-4-444-200000000000022-22-2-2223−23−2323−232323−230000004-4000000000000000023−23−2323-222-20000000000000000000000000000000000000000
χ1064-4-44-4-444-200000000000022-22-2-2223−23−2323−232323−23000000-440000000000000000−232323−232-2-220000000000000000000000000000000000000000
χ1074-4-44-4-444-200000000000022-22-2-22−232323−2323−23−23230000004-40000000000000000−232323−23-222-20000000000000000000000000000000000000000
χ1084-4-44-4-444-200000000000022-22-2-22−232323−2323−23−2323000000-44000000000000000023−23−23232-2-220000000000000000000000000000000000000000

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