Finite Group Databasebeta

← Group #13156581

Character table — Group #13156581

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111222222222222224444444444444444444444666688888888888812121212121212121212121212121212181818182424242424242424242424242424242424243636363654545454727272727272
order122233344666666666333666666666121212121212121212128888366612121212121212122424242424242424242424242424242444444412121212121212121212121212121212121212128888226666
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-111
χ51111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-11111-11-1-111
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-111111-111-1-1
χ92222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-200002222-2-2-2-2-2-2-2-2000000000000000022-2-200000000000000000022-2-20000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-200002222-2-2-2-2-2-2-2-20000000000000000-2-222000000000000000000-2-2220000000000
χ11222222-12222-1-12-12222-1-122-1-1-1-1-12-12-122-1-12-1-1-12222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000200-1-100220000-1-1-1-1000000000200-1-1
χ12222222-12222-1-12-12222-1-122-1-1-1-1-12-12-122-1-12-1-1-12222-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000-2001100-2-200001111000000000-20011
χ13222222-12222-1-12-12222-1-122-1-1-1-1-12-12-122-1-12-1-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111111100000200-1-100220000-1-1-1-1000000000-20011
χ14222222-12222-1-12-12222-1-122-1-1-1-1-12-12-122-1-12-1-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111111100000-2001100-2-200001111000000000200-1-1
χ1522222-1222-1-122-12222-12-1-1-122-1-1-1-12-1222-1-1-12-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000020-1-1002200-1-1-1-100000000000020-1-100
χ1622222-1222-1-122-12222-12-1-1-122-1-1-1-12-1222-1-1-12-1-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-201100-2-2001111000000000000-201100
χ1722222-1222-1-122-12222-12-1-1-122-1-1-1-12-1222-1-1-12-1-1-2-2-2-2-1-1-1-1-1-122-1-1-1-11111-2-2-2-211111111000020-1-1002200-1-1-1-1000000000000-201100
χ1822222-1222-1-122-12222-12-1-1-122-1-1-1-12-1222-1-1-12-1-1-2-2-2-2-1-1-1-1-1-122-1-1-1-11111-2-2-2-2111111110000-201100-2-200111100000000000020-1-100
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.