Finite Group Databasebeta

← Group #13168064

Character table — Group #13168064

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size1111222222222222444444444444466668888888888888888812121212121212121212121212121212181818182424242424242424242424242424242424243636363636363636363654545454727272
order12223336666666663334666666666224436661212121212121212121212121222446666661212121212122244666666666121212121212121212444466121212124444121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-11111-1-111-1-111-1-1-1-1-111-1-111111-1111-1-11111-1-1-1-111-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111-1-11111111111111111111-11111111-1-111-1-111-1-1111111111-11-1-1-111-1-1-1-11-111-1-1-1-1-1-1-1-1-11-1
χ41111111111111111111111111111111-1-1111111111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-111-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-11
χ511111111111111111111111111111-1-11111111111111111111-1111-1-1-1-111111111-1-1111-1-111-1-1-1-1111111111-1-1-11-1-1-1-111-1-1-1-1-1-11
χ611111111111111111111111111111-1-11111111111111111111-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-1-11-111-1-1-1-11111-11-1
χ711111111111111111111111111111-1-1-1-111111111111111111-11-11-1-1-1-111-1-111-1-1-1-1-1-11-1-111-1-1-1-1-11-1-1-111-1-111-1-1-1-111-1-111111-1-1
χ811111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111
χ91111111111111111111-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111-1-11111-1-11-1-11111-1-1-1-1-1-1-1-1-1111-1-111111-1-1-1-111-1-11
χ101111111111111111111-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1-111-1-1-1-1-111-1-1-11-1-1-111111-11-1-1-1111111-1-1-11-1
χ111111111111111111111-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-111111-1-11111-1-11-1111-1-1-1-1-11-1-111-1-11111-1-11-1-1
χ121111111111111111111-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-11111111-1-1-1111-1-1-1-1-1-1-1-111111
χ131111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-111111-1-111-1-1-1-1-1-1-111-1111-1-1-1-1-1-111-1-1111
χ141111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-11111111111-111-1-1-1-111-11-1-1-11111-11-1-111-1-111-1-1111-1-1
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1111-1111-1-1-1-11-11-1-1-11111-1-111-11-1
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-1-111-1-111-1-1-111-1-1-1-1111111111-1-11-1-111111-1-111-1-1-1-11
χ17222222-1-12-1222-1222-1-122-1-1-1-1-12-122200-1-1-1-1-122-1-1-1-122-1-1-1-1220222-1-1-1-1002200220022-1-1-1-1-1-1-10-1000-1-1000020-1-1000000000-10
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χ3022222-122-1222-12-12-12-1-2-12-1-12-1-12-122-2-2-1-1-1-1-2-21-2-211111111-2020-1-12200-2-20011000001-200-1-111-102-1-10011-22000011000000-100
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χ362222-122222-1-1222-1-1-122-1-122-12-1-1-100-2-2-1-1-1-12-12-1-122-1-1-1-1-1-10-2-2-20000-2-21111-2-20022100110000-2-2111111100020000-1-1000000-1
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χ1038-8-88-4-48-84-844-484-42-4-402-44-444-24-200002-22-200000000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-444444-4-44-4222022-22-2-2-2-2-20000-11-110006i−6i0000−3i3i3i−3i0000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-444444-4-44-4222022-22-2-2-2-2-20000-11-11000−6i6i00003i−3i−3i3i0000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).