Finite Group Databasebeta

← Group #10690746

Character table — Group #10690746

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order12222222222234444666666644666688888888121212124444444444441212121212121212121224242424242424244444888888884412121212444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ911111111-1-1-1-11-1-1-1-1111111111-1-1-1-1iiii−i−i−i−i-1-1-1-11111-1-1-1-1ii−i−i11iiii−i−i−i−iiiii−i−i−i−i-1-111iiii−i−i−i−i1-111-1-1ii−i−i1-1
χ1011111111-1-1-1-11-1-1-1-1111111111-1-1-1-1iiii−i−i−i−i-1-1-1-11111-1-1-1-1−i−iii11−i−i−i−iiiiiiiii−i−i−i−i-1-111iiii−i−i−i−i-11-1-111−i−iii-11
χ1111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-11111ii−i−i11iiii−i−i−i−iiiii−i−i−i−i11-1-1−i−i−i−iiiii1-111-1-1−i−iii-11
χ1211111111-1-1-1-11-1-1-1-1111111111-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-11111−i−iii11−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−i−i−iiiii-11-1-111ii−i−i1-1
χ1311111111-1-1-1-11-1-1-1-1111111111-1-1-1-1−i−i−i−iiiii-1-1-1-11111-1-1-1-1ii−i−i11iiii−i−i−i−i−i−i−i−iiiii-1-111−i−i−i−iiiii-11-1-111ii−i−i-11
χ1411111111-1-1-1-11-1-1-1-1111111111-1-1-1-1−i−i−i−iiiii-1-1-1-11111-1-1-1-1−i−iii11−i−i−i−iiiii−i−i−i−iiiii-1-111−i−i−i−iiiii1-111-1-1−i−iii1-1
χ1511111111-1-1-1-11-1-1-1-1111111111-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-11111ii−i−i11iiii−i−i−i−i−i−i−i−iiiii11-1-1iiii−i−i−i−i-11-1-111−i−iii1-1
χ1611111111-1-1-1-11-1-1-1-1111111111-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-11111−i−iii11−i−i−i−iiiii−i−i−i−iiiii11-1-1iiii−i−i−i−i1-111-1-1ii−i−i-11
χ172222222222222-2-2-2-22222222-2-2222200000000-2-2-2-22222-2-2-2-20000-2-2000000000000000022-2-200000000000000000000
χ182222222222222-2-2-2-22222222-2-2222200000000-2-2-2-2-2-2-2-222220000-2-20000000000000000-2-22200000000000000000000
χ19222222222222-12222-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ20222222222222-12222-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-100000000-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ21222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ22222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-100000000-2-2-2-2-1-1111111111111111100000000000022-1-1-1-1000000
χ2322222222-2-2-2-2222222222222-2-2-2-2-2-2000000002222222222220000-2-20000000000000000-2-2-2-200000000000000000000
χ2422222222-2-2-2-2222222222222-2-2-2-2-2-2000000002222-2-2-2-2-2-2-2-20000-2-20000000000000000222200000000000000000000
χ2522222222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-12211112i2i2i2i−2i−2i−2i−2i1111000000002i2i−2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii0000000000002-2-1-111000000
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χ32222-2-22-2-222-2-220000222-2-2-2-20022-2-2−2−222−2−2220000-2-222000000000000000000−2−222−2−222-220022−2−222−2−2000000000000
χ33222-2-22-2-2-2-22220000222-2-2-2-200-2-222−i2−i2i2i2i2i2−i2−i2000022-2-2000000000000000000−i2−i2i2i2i2i2−i2−i2-2200−i2−i2i2i2i2i2−i2−i2000000000000
χ34222-2-22-2-2-2-22220000222-2-2-2-200-2-222−i2−i2i2i2i2i2−i2−i20000-2-222000000000000000000−i2−i2i2i2i2i2−i2−i22-200i2i2−i2−i2−i2−i2i2i2000000000000
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χ3822-22-2-2-22000022i−2i2i−2i2-2-222-2-2000000000000002i−2i2i−2i2i−2i2i−2i22-2-2−1−i1+i−1+i1−i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000000000000000−1+i1−i−1−i1+i00
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χ4322-22-2-2-2200002−2i2i−2i2i2-2-222-2-200000000000000−2i2i−2i2i−2i2i−2i2i22-2-21−i−1+i1+i−1−i001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000000000000000001+i−1−i1−i−1+i00
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χ482-2-2222-2-22-22-220000-22-2-222-2002-2-22−22−22−22−2200000000−2i2i−2i2i00000000000000−22−22−22−2200−2i2i−i2i2−i2i2−i2i2−i2i2000000000000
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χ904-4-4444-4-44-44-4-200002-222-2-2200-222-2−2222−2222−2222−2222000000000000000000000000002−22−22−22−2000000000000000000000000
χ914-4-4444-4-4-44-44-200002-222-2-22002-2-22−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ924-4-4444-4-4-44-44-200002-222-2-22002-2-222i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ934-4-4-4-44444-4-44-244-4-42-22-222-24-4-22-2200000000-2-222000000000000-220000000000000000000000000000000000000000
χ944-4-4-4-4444-444-4-2-4-4442-22-222-24-42-22-20000000022-2-2000000000000-220000000000000000000000000000000000000000
χ9588-8-88-88-80000-40000-44444-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ968-888-8-88-80000-4000044-44-44-4000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.