Finite Group Databasebeta

← Group #10690670

Character table — Group #10690670

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
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χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-111-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-111-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1111-1-11-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111111111111-1-1111-1-11-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ91111-1-1-1-111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iii−i−iii−i−iii−i−i
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χ864-44-44i−4i−4i4i0040000000000-44-44i−4i4i−4i00000000000000000000000000000000000000000000000000−2−2i2+2i00−2+2i2−2i000000000000
χ874-44-4−4i4i4i−4i0040000000000-44-4−4i4i−4i4i000000000000000000000000000000000000000000000000002−2i−2+2i002+2i−2−2i000000000000
χ884-44-4−4i4i4i−4i0040000000000-44-4−4i4i−4i4i00000000000000000000000000000000000000000000000000−2+2i2−2i00−2−2i2+2i000000000000
χ894-4-4444-4-40040000000000-4-444-4-44000000000000000000000000000000000000000000000000−2i22i200−2i22i200000000000000
χ904-4-4444-4-40040000000000-4-444-4-440000000000000000000000000000000000000000000000002i2−2i2002i2−2i200000000000000
χ914-4-44-4-4440040000000000-4-44-444-400000000000000000000000000000000000000000000000022−2200−222200000000000000
χ924-4-44-4-4440040000000000-4-44-444-4000000000000000000000000000000000000000000000000−22220022−2200000000000000
χ938-88-88i−8i−8i8i00-400000000004-44−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ948-88-8−8i8i8i−8i00-400000000004-444i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ958-8-8888-8-800-4000000000044-4-444-400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88-8-88800-4000000000044-44-4-4400000000000000000000000000000000000000000000000000000000000000000000

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