Finite Group Databasebeta

← Group #13166329

Character table — Group #13166329

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222244444444444444444466668888888888888888999912121212121212121212121212121212181818181818363636363636363636363636363654545454108108108108
order1222344666336666661212121212121212121244443366666612121212121212124444121212121212121212121212121212122212121212668888242424242424242444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-1ii−i−i
χ4111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-1−i−iii
χ51111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1111−i−iii
χ81111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii1111ii−i−i
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χ948-8-88-48i−8i4-44-424-24-2-42−4i4i−4i−4i2i2i4i4i−2i−2i00002-1-212-1-212i2i−i−i−2i−2iii000000000000000000000000000000000000000000000000
χ958-8-88-4−8i8i4-442-4-24-242-44i−4i−2i−2i4i4i2i2i−4i−4i0000-121-2-121-2ii−2i−2i−i−i2i2i000000000000000000000000000000000000000000000000
χ968-8-88-4−8i8i4-44-424-24-2-424i−4i4i4i−2i−2i−4i−4i2i2i00002-1-212-1-21−2i−2iii2i2i−i−i000000000000000000000000000000000000000000000000

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