Finite Group Databasebeta

← Group #13168675

Character table — Group #13168675

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size1111222222222222224444444444444444448888888888888812121212121218181818181824242424242424242424242424242424242424242424242436363636363636363636363636363654545454
order122233344666666666333666666666121212121212366612121212121212121212244444444444666612121212121212121212121212121212121212124441212121212121212121212122244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-11-1111-1-1-1-111111-11-1111-11-11111-1-111-1-1-11-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-11-111-1-111-1-11111-11-1111-11-1111-1-111-1-111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111111111111111111111-11111-1-1-1-1-111-1-1-1-11111-1-11111-1-1111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1
χ611111111111111111111111111111111111111111111111111-11-11-1-1-1-111-1-1-1-1-1-11-11-1-1-11-11-1-1-111-1-111-1-1-1-11-1-1-1-1-1-11111-1-11111
χ711111111111111111111111111111111111111111111111111-1-11-11-111-1-1-1-1-1-1-1-1-11-11-1-1-11-11-1-1-1-111-1-111-11-1-1-11111-1-1-1-1-1-11111
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1
χ91111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-111-1-1-1-1-1-111
χ101111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11-111-1-1-1-111111-11-1-1-1-11-11-1-1-1-11111-1-11-11-1-111-1-1-1-1111111-1-1
χ111111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-11111-11-11-1-11-11-1-1-111-1-1-1-11111-1-1-1-1-11111-1-11111-1-1
χ121111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-1-1-1-11111-1-111-1-111-1-1-1-111
χ131111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-11111-11111-1-111-1-111-1-111-1-1
χ141111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-1-1-11-11-111-11-1111-1-11111-1-111-1-1-1-1-11111-1-111-1-111
χ151111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1-1-1-1-1-1-1-11-11111-11-11111-1-1-1-1111-11-1-111-1-1-1-11111-1-111
χ161111111-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1
χ17222222-1222-12222-1-122-1-12-1-1-12-1-12-122-1-122-1-1-1-1-1-122-1-1-1-1-1-12020220022002-1-1-10-1022-10-102-1-100-1-100-1-1002000000-1-1-1-1000000
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χ19222222-1222-12222-1-122-1-12-1-1-12-1-12-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1-20202-200-2-200-21110-102-210-1021100-1-100-1-100-20000001111000000
χ20222222-1222-12222-1-122-1-12-1-1-12-1-12-122-1-122-1-1-1-1-1-122-1-1-1-1-1-1-20-20-2-2002200-2111010-2-21010-21100110011002000000-1-1-1-1000000
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χ2822222-1222-1222-1-1222-12-1-12-1-1-12-1-12-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-20-20-22200001-21110-201-210-20111100110002000-1-1-1-10000000000
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χ432-22-2222−2i2i-2-2-2-22-22-22222-2-22-222-2-2-2−2i2i−2i2i−2i2i22-2-2−2i2i−2i2i−2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000000002-2−2i2i
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χ9688-8-8-4-4800-48-4444-8-842-4-4-244-4-2442-40000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-4-400-4-4-4444444222-2-2-22-2-2-222000000-111-1000000−3i33i3−3i33i30000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-400-4-4-4444444222-2-2-22-2-2-222000000-111-10000003i3−3i33i3−3i30000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-48i−8i4444-44-44-4222-2-22-222-2-2-2−4i4i−4i4i−4i4i-1-1112i−2i2i−2i2i−2i−i−iii0000000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-4−8i8i4444-44-44-4222-2-22-222-2-2-24i−4i4i−4i4i−4i-1-111−2i2i−2i2i−2i2iii−i−i0000000000000000000000000000000000000000000000000000000
χ1018-8-888-4-40044-884-44-4-8-4-42-4-4-2-2442440000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1028-8-88-48-400-844-4-884-44-42-4-42444-2-44-20000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-48004-84-44-4-8842-4-42-444-24-4-240000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-400444-44-44-4422222-2-2-2-22-2-2000000-11-1100000033−33−33330000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-400444-44-44-4422222-2-2-2-22-2-2000000-11-11000000−333333−330000000000000000000000000000000000000000000000000000000

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