Finite Group Databasebeta

← Group #10690539

Character table — Group #10690539

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order12222222444444443444444446666666121212121212121222444444666612121212121212121212121212121212121212124444444412121212121212121212121212121212888888888888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii
χ1722222222222222222-2-2-2-2-2-2-2-22222222222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ1822222222222222222-2-2-2-2-2-2-2-2222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000000000000000
χ192222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ202222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ212222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-1-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ222222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111-1-1-1-1-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ232222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ242222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ252222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ262222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22-2-2-2-222222222222-2-2-2-2-2-2-2-222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-22-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000
χ2922222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111122-2-222-2-2-1-1-1-11111-1-1-1-11111000000000000000000000000
χ3022222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-11111-2-222-2-2221111-1-1-1-11111-1-1-1-1000000000000000000000000
χ3122222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-111111111-2-222-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-1000000000000000000000000
χ3222222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-111111111-2-222-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-11111000000000000000000000000
χ3322222222-2-2-2-2-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-11111111122-2-2-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3000000000000000000000000
χ3422222222-2-2-2-2-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-11111111122-2-2-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3000000000000000000000000
χ3522222222-2-2-2-2-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000000000000000000000000
χ372222-2-2-2-22222-2-2-2-2200000000222-2-2-2-22222-2-2-2-22-22-2000022-2-222-2-2000000000000000000000000000000000000000022−2−222−2−222−2−222−2−200000000
χ382222-2-2-2-22222-2-2-2-2200000000222-2-2-2-22222-2-2-2-22-22-2000022-2-222-2-20000000000000000000000000000000000000000−2−222−2−222−2−222−2−22200000000
χ392222-2-2-2-22222-2-2-2-2200000000222-2-2-2-22222-2-2-2-2-22-220000-2-222-2-222000000000000000000000000000000000000000022−2−222−2−2−2−222−2−22200000000
χ402222-2-2-2-22222-2-2-2-2200000000222-2-2-2-22222-2-2-2-2-22-220000-2-222-2-2220000000000000000000000000000000000000000−2−222−2−22222−2−222−2−200000000
χ412222-2-2-2-2-2-2-2-22222200000000222-2-2-2-2-2-2-2-222222-2-22000022-2-2-2-2220000000000000000000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000
χ422222-2-2-2-2-2-2-2-22222200000000222-2-2-2-2-2-2-2-222222-2-22000022-2-2-2-2220000000000000000000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000
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χ4722-2-22-22-22i2i−2i−2i2i2i−2i−2i2-2-222−2i2i−2i2i2-2-22-22-22i2i−2i−2i2i2i−2i−2i0000000000000000-2-222−2i−2i2i2i000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ4822-2-22-22-22i2i−2i−2i2i2i−2i−2i2-2-222−2i2i−2i2i2-2-22-22-22i2i−2i−2i2i2i−2i−2i0000000000000000-2-222−2i−2i2i2i0000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
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χ5122-2-22-22-2−2i−2i2i2i−2i−2i2i2i2-2-2222i−2i2i−2i2-2-22-22-2−2i−2i2i2i−2i−2i2i2i0000000000000000-2-2222i2i−2i−2i0000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
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χ652-22-2-222-2−2i2i−2i2i−2i2i−2i2i22-22-2−2i2i2i−2i-22-2-222-2−2i2i−2i2i−2i2i−2i2i00000000000000002-22-2−2i2i−2i2i0000000000002i−2i-22000000002i−2i2i−2i-22-22000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.