Finite Group Databasebeta

← Group #10746850

Character table — Group #10746850

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111111111111222222222222222244444444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order122222222222222236666666666666662222444444446666666612121212121212121212121212121212222244446666666612121212121212122244444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-1
χ911111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1
χ1011111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111
χ1111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1
χ1211111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-111
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11111-1-1-1-1
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-11111
χ172222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ192222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ202222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-222-2-2221111-1-1-1-11111-1-1-1-10000000000000000
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χ232222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ242222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-111110000000000000000
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χ4122-2-2222-2-22-2-222-2-222-2-222-2-22222-2-2-2-2000000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000002-200002i−2i00
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χ4522-2-22-2-2222-2-2-2-22222-2-222-2-2-2-2-2-222222-22-222-2-22-2-2222-2-222-2-222-2-222-2-22-22-2-22-220000000000000000000000000000000000000000
χ4622-2-22-2-2222-2-2-2-22222-2-222-2-2-2-2-2-222222-22-2-2-222-222-222-2-222-2-2-2-222-2-222-22-222-22-20000000000000000000000000000000000000000
χ4722-2-22-2-2222-2-2-2-22222-2-222-2-2-2-2-2-22222-22-2222-2-2-222-2-2-222-2-22222-2-222-2-2-22-222-22-20000000000000000000000000000000000000000
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χ5122-2-22-2-2222-2-2-2-222-1-111-1-1111111-1-1-1-12-22-2-2-222-222-2-1-111-1-11111-1-111-1-11-11-1-11-1100000000−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i30000000000000000
χ5222-2-22-2-2222-2-2-2-222-1-111-1-1111111-1-1-1-12-22-2-2-222-222-2-1-111-1-11111-1-111-1-11-11-1-11-1100000000i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i30000000000000000
χ5322-2-22-2-2222-2-2-2-222-1-111-1-1111111-1-1-1-1-22-2222-2-2-222-211-1-111-1-1-1-111-1-1111-11-1-11-1100000000−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i30000000000000000
χ5422-2-22-2-2222-2-2-2-222-1-111-1-1111111-1-1-1-1-22-2222-2-2-222-211-1-111-1-1-1-111-1-1111-11-1-11-1100000000i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i30000000000000000
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χ5722-2-2-222-22-222-2-2-2222-2-2-2-222-2-222-2-2222-2-220000000022-2-2-2-2220000000000000000002-2002-200002-2-2200002-2-220000000000000000
χ5822-2-2-222-22-222-2-2-2222-2-2-2-222-2-222-2-2222-2-220000000022-2-2-2-222000000000000000000-2200-220000-222-20000-222-20000000000000000
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χ6222-2-2-222-22-222-2-2-22-1-11111-1-111-1-111-1-12-2-2200000000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i3i3i3−i3i3−i3−i3i300-2200-22i3−i3−i3i31-1-11i3−i3−i3i31-1-110000000000000000
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χ8644-4-4-4-4-44-4-444444-4-2-22222-2-2-2-222-2-2220000000000000000000000000000−232323−23−232323−230000000000000000000000000000000000000000
χ874-44-444-4-44-4-44-444-44-44-4-44-44-444-44-4-440000000000000000000000000000000000000000000000000000000000000000000000000000
χ884-44-444-4-44-4-44-444-4-22-222-22-22-2-22-222-2000000000000−2i32i3−2i32i3−2i32i3−2i32i300000000000000000000000000000000000000000000000000000000
χ894-44-444-4-44-4-44-444-4-22-222-22-22-2-22-222-20000000000002i3−2i32i3−2i32i3−2i32i3−2i300000000000000000000000000000000000000000000000000000000
χ904-44-44-444-4-4-444-4-444-44-4-44-444-4-44-444-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ914-44-44-444-4-4-444-4-44-22-222-22-2-222-22-2-2200000000000000000000−2i32i3−2i32i32i3−2i32i3−2i3000000000000000000000000000000000000000000000000
χ924-44-44-444-4-4-444-4-44-22-222-22-2-222-22-2-22000000000000000000002i3−2i32i3−2i3−2i32i3−2i32i3000000000000000000000000000000000000000000000000
χ934-44-4-44-4-4-444-44-444-22-22-22-22-22-22-22-2200004-44-4000000000000-22-22-22-22000000000000000000000000000000000000000000000000
χ944-44-4-44-4-4-444-44-444-22-22-22-22-22-22-22-220000-44-440000000000002-22-22-22-2000000000000000000000000000000000000000000000000
χ954-44-4-4-444444-4-44-4-44-44-44-44-4-44-44-44-440000000000000000000000000000000000000000000000000000000000000000000000000000
χ964-44-4-4-444444-4-44-4-4-22-22-22-222-22-22-22-2000000000000−2i32i3−2i32i32i3−2i32i3−2i300000000000000000000000000000000000000000000000000000000
χ974-44-4-4-444444-4-44-4-4-22-22-22-222-22-22-22-20000000000002i3−2i32i3−2i3−2i32i3−2i32i300000000000000000000000000000000000000000000000000000000
χ984-4-4444-44-4-44-4-44-444-4-44-444-4-444-4-444-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ994-4-4444-44-4-44-4-44-44-222-22-2-222-2-222-2-2200000000000000000000−2i32i32i3−2i32i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ1004-4-4444-44-4-44-4-44-44-222-22-2-222-2-222-2-22000000000000000000002i3−2i3−2i32i3−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ1014-4-444-44-44-44-44-44-44-4-44-444-44-4-444-4-440000000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-444-44-44-44-44-44-4-222-22-2-22-222-2-222-2000000000000−2i32i32i3−2i3−2i32i32i3−2i300000000000000000000000000000000000000000000000000000000
χ1034-4-444-44-44-44-44-44-4-222-22-2-22-222-2-222-20000000000002i3−2i3−2i32i32i3−2i3−2i32i300000000000000000000000000000000000000000000000000000000
χ1044-4-44-44-4444-444-4-4-44-4-444-4-444-44-4-44-440000000000000000000000000000000000000000000000000000000000000000000000000000
χ1054-4-44-44-4444-444-4-4-4-222-2-222-2-22-222-22-2000000000000−2i32i32i3−2i32i3−2i3−2i32i300000000000000000000000000000000000000000000000000000000
χ1064-4-44-44-4444-444-4-4-4-222-2-222-2-22-222-22-20000000000002i3−2i3−2i32i3−2i32i32i3−2i300000000000000000000000000000000000000000000000000000000
χ1074-4-44-4-44-4-44-44-4444-222-2-222-22-22-2-22-2200004-4-44000000000000-222-2-222-2000000000000000000000000000000000000000000000000
χ1084-4-44-4-44-4-44-44-4444-222-2-222-22-22-2-22-220000-444-40000000000002-2-222-2-22000000000000000000000000000000000000000000000000

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