Finite Group Databasebeta

← Group #10855224

Character table — Group #10855224

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222444444444444444444444444444444444488888888888888888888888888121212121212121224242424242424244848
order1222222234444444466666662222444444666666661212121212121212121212121212121244444444121212121212121212121212121212121212888888882244888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111-1-111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ91111111111-1-1-1-11111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ101111111111-1-1-1-11111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-11
χ121111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1111-1
χ131111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11111-111-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-111-11
χ141111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11111-111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-11111-1-11-1
χ151111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1111-1-11111-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ161111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1111-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ17222222222-22222-2-2-22222222000022-2-22200000000-2-2-2-2222222222222-2000000-2-2-20000-2-20000-2-20000000000000000000000
χ18222222222-22222-2-2-222222220000-2-2-2-2-2-200000000-2-2-2-2-2-2-2-22222-2-2-2-220000002220000-2-20000220000000000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222200002222-2-200000000-2-2-2-22222-2-2-2-2-2-2-2-2-20000002-2-20000220000220000000000000000000000
χ20222222222-2-2-2-2-2-2-2-222222220000-2-2222200000000-2-2-2-2-2-2-2-2-2-2-2-222222000000-2220000220000-2-20000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ2222222222-122222222-1-1-1-1-1-1-12222-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-2-2-2-2-222-2111111-1-1-1-1-1-1111111000000000000000000
χ2322222222-122222222-1-1-1-1-1-1-1-2-2-2-222222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2-2-2-2-22-1-11111-1-11111-1-11111000000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-211111111-1-1-1-11111-1-1-1-11111-22222-2-2-211-1-1-1-1-1-1111111-1-1-1-1000000000000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111222-2-2-2-2-2-1-1-1-1-1-1111111111111000000000000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-12222-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-2-2-222-2-22111111111111-1-1-1-1-1-1000000000000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-211111111-1-1-1-1-1-1-1-1111111112-2-22222-2-1-1111111-1-1-1-111-1-1-1-1000000000000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22211111111-1-1-1-111111111-1-1-1-1-222-2-222211-1-1-1-111-1-1-1-1-1-11111000000000000000000
χ2922222222-1-22222-2-2-2-1-1-1-1-1-1-1000022-2-222−i3−i3−i3−i3i3i3i3i31111-1-1-1-1-1-1-1-1-1-1-1-1-2000000-211−i3−i3i3i311−i3−i3i3i311−i3−i3i3i3000000000000000000
χ3022222222-1-22222-2-2-2-1-1-1-1-1-1-1000022-2-222i3i3i3i3−i3−i3−i3−i31111-1-1-1-1-1-1-1-1-1-1-1-1-2000000-211i3i3−i3−i311i3i3−i3−i311i3i3−i3−i3000000000000000000
χ3122222222-1-22222-2-2-2-1-1-1-1-1-1-10000-2-2-2-2-2-2−i3−i3−i3−i3i3i3i3i311111111-1-1-1-1111120000002-1-1i3i3−i3−i311−i3−i3i3i3-1-1i3i3−i3−i3000000000000000000
χ3222222222-1-22222-2-2-2-1-1-1-1-1-1-10000-2-2-2-2-2-2i3i3i3i3−i3−i3−i3−i311111111-1-1-1-1111120000002-1-1−i3−i3i3i311i3i3−i3−i3-1-1−i3−i3i3i3000000000000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-100002222-2-2−i3−i3−i3−i3i3i3i3i31111-1-1-1-111111111-2000000211−i3−i3i3i3-1-1i3i3−i3−i3-1-1i3i3−i3−i3000000000000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-100002222-2-2i3i3i3i3−i3−i3−i3−i31111-1-1-1-111111111-2000000211i3i3−i3−i3-1-1−i3−i3i3i3-1-1−i3−i3i3i3000000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-10000-2-22222−i3−i3−i3−i3i3i3i3i3111111111111-1-1-1-12000000-2-1-1i3i3−i3−i3-1-1i3i3−i3−i311−i3−i3i3i3000000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-10000-2-22222i3i3i3i3−i3−i3−i3−i3111111111111-1-1-1-12000000-2-1-1−i3−i3i3i3-1-1−i3−i3i3i311i3i3−i3−i3000000000000000000
χ37222-2-22-2-2202i2i−2i−2i0002-22-2-22-200002i−2i002-20000000000002i2i−2i−2i2i2i−2i−2i22-2-200000000000000000000000000−i2−i2i2i222−2−20000−i2i22−200
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χ39222-2-22-2-2202i2i−2i−2i0002-22-2-22-20000−2i2i00-22000000000000−2i−2i2i2i2i2i−2i−2i-2-22200000000000000000000000000−i2−i2i2i222−2−20000i2−i2−2200
χ40222-2-22-2-2202i2i−2i−2i0002-22-2-22-20000−2i2i00-22000000000000−2i−2i2i2i2i2i−2i−2i-2-22200000000000000000000000000i2i2−i2−i2−2−2220000−i2i22−200
χ41222-2-22-2-220−2i−2i2i2i0002-22-2-22-200002i−2i00-220000000000002i2i−2i−2i−2i−2i2i2i-2-22200000000000000000000000000−i2−i2i2i2−2−2220000i2−i22−200
χ42222-2-22-2-220−2i−2i2i2i0002-22-2-22-200002i−2i00-220000000000002i2i−2i−2i−2i−2i2i2i-2-22200000000000000000000000000i2i2−i2−i222−2−20000−i2i2−2200
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χ4622-22-2-22-22-200002-2222-22-2-2-222-2-200000022-2-222-2-222-2-200000000000000000000000000000000000000−2i2i−2i2i000000−2i2i000000
χ4722-22-2-22-22-200002-2222-22-2-2-2-2-222000000-2-222-2-22222-2-2000000000000000000000000000000000000002i−2i2i−2i000000−2i2i000000
χ4822-22-2-22-22-200002-2222-22-2-2-2-2-222000000-2-222-2-22222-2-200000000000000000000000000000000000000−2i2i−2i2i0000002i−2i000000
χ492-2222-2-2-2222i−2i2i−2i-2-22-2-2222-2-22-22-2002i−2i002-22-22-22-22-22-200002i−2i2i−2i0000000002i−2i00000002i−2i2i−2i2i−2i000000000000000000000000
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χ552-2222-2-2-22-2−2i2i−2i2i22-2-2-2222-2-20000002i−2i0000000000-22-220000−2i2i−2i2i000002-2−2i2i000002-22-22i−2i000000−2i2i−2i2i000000000000000000
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χ8644-4-44-4-444000000004-4-4-44-4400000000000000000000000000000000000000000000000000000000000022−22−222200000000000000
χ8744-4-44-4-444000000004-4-4-44-44000000000000000000000000000000000000000000000000000000000000−222222−2200000000000000
χ884-44-4-4-444404-4-44000-444-4-4-44000000000000000000000000004-4-44000000000000000000000000000000000000000000000000
χ894-44-4-4-44440-444-4000-444-4-4-4400000000000000000000000000-444-4000000000000000000000000000000000000000000000000
χ904-44-4-4-444-204-4-440002-2-2222-2000000000000000000000023−23−2323-222-2−232323−2300000000000000000000000000000000000000000000
χ914-44-4-4-444-204-4-440002-2-2222-20000000000000000000000−232323−23-222-223−23−232300000000000000000000000000000000000000000000
χ924-44-4-4-444-20-444-40002-2-2222-2000000000000000000000023−23−23232-2-2223−23−232300000000000000000000000000000000000000000000
χ934-44-4-4-444-20-444-40002-2-2222-20000000000000000000000−232323−232-2-22−232323−2300000000000000000000000000000000000000000000
χ944-4-44-44-444400004-4-4-4-4-44-444000000000000000000-444-400000000000000000000000000000000000000000000000000000000
χ954-4-44-44-44-2400004-4-4222-22-2-20000000000−2i32i32i3−2i32i3−2i3−2i32i32-2-2200000000000000000000000000000000000000000000000000000000
χ964-4-44-44-44-2400004-4-4222-22-2-200000000002i3−2i3−2i32i3−2i32i32i3−2i32-2-2200000000000000000000000000000000000000000000000000000000
χ974-4-44-44-44-2-40000-444222-22-2-24-4-44000000-222-2-222-2-222-200000000000000000000000000000000000000000000000000000000
χ984-4-44-44-44-2-40000-444222-22-2-2-444-40000002-2-222-2-22-222-200000000000000000000000000000000000000000000000000000000
χ994-4-4-4444-4400000000-44-4-444-4000000000000000000000000000000000000000000000000000000000000000022−22−22220000000000
χ1004-4-4-4444-4400000000-44-4-444-40000000000000000000000000000000000000000000000000000000000000000−222222−220000000000
χ10188-8-88-8-88-400000000-4444-44-4000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-8-8888-8-4000000004-444-4-44000000000000000000000000000000000000000000000000000000000000000000000000000000

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