Finite Group Databasebeta

← Group #72341879

Character table — Group #72341879

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
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χ611-1-11-1-11ii−i−i111-1-1-1111-1-1-11-11-111111-1-1-1-1-1iiiiiiiiii−i−i−i−i−i−i−i−i−i−i1111-1-1-1-1-1-111iiii−i−i−i−i-11−ii-1-1-1111−i−i−iiii
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χ8166-66-60003i2−3i2−3i23i2-2-2-2222222-2-2-2-222-2000−4i4i0004i−4i−i2−i2−i23ζ5−ζ7+3ζ13−ζ23−ζ5+3ζ7−ζ13+3ζ23i2i2i2−3ζ5+ζ7−3ζ13+ζ23ζ5−3ζ7+ζ13−3ζ23i2i2i2−3ζ5+ζ7−3ζ13+ζ23ζ5−3ζ7+ζ13−3ζ23−i2−i2−i23ζ5−ζ7+3ζ13−ζ23−ζ5+3ζ7−ζ13+3ζ23000000000000000000000000000000000000
χ8266-6-6666-600006-2-2-6226-2-2-622-22-22-622226-2-2-2-200000000000000000000000000000000000000000000000000000000
χ8366-6-6666-60000-26-22-62-26-22-62-22-222-6222-26-2-2-200000000000000000000000000000000000000000000000000000000
χ8466-6-6666-60000-2-2622-6-2-2622-6-22-2222-622-2-26-2-200000000000000000000000000000000000000000000000000000000
χ8566-6-6666-60000-2-2-2222-2-2-22222-22-2222-2-2-2-2-2220004-40004-4000-44000-44000000000000000000000000000000000000
χ8666-6-6666-60000-2-2-2222-2-2-22222-22-2222-2-2-2-2-222000-44000-440004-40004-4000000000000000000000000000000000000
χ8766-6-66-6-666i6i−6i−6i-2-2-2222-2-2-22222-22-2-2-2-222222-2-2−2i−2i−2i2i2i−2i−2i−2i2i2i2i2i2i−2i−2i2i2i2i−2i−2i000000000000000000000000000000000000
χ8866-6-66-6-66−6i−6i6i6i-2-2-2222-2-2-22222-22-2-2-2-222222-2-22i2i2i−2i−2i2i2i2i−2i−2i−2i−2i−2i2i2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ8916-16000−8i28i20000000000000000000000000000000000000000000000000004-400−2i22i2−2i22i20000000000000000000000000000
χ9016-16000−8i28i2000000000000000000000000000000000000000000000000000-2223−232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ230000000000000000000000000000
χ9116-16000−8i28i2000000000000000000000000000000000000000000000000000-22−23232ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ70000000000000000000000000000
χ9216-160008i2−8i20000000000000000000000000000000000000000000000000004-4002i2−2i22i2−2i20000000000000000000000000000
χ9316-160008i2−8i2000000000000000000000000000000000000000000000000000-2223−23−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ230000000000000000000000000000
χ9416-160008i2−8i2000000000000000000000000000000000000000000000000000-22−2323−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ70000000000000000000000000000

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