Finite Group Databasebeta

← Group #13169335

Character table — Group #13169335

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222444444444444444444444666666666688888888888881212121212121212121212121212121212121212121212121218181818242424242424242424242424363636363636363636365454727272108
order1222333666666666333466666666612121212121212124444441212121236661212121212121212124441212121212121212121212121212121212121212121244441212121212121212121212124444121212121212441212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-11111111111-1-1111111111111-1-11-1-1-11111-1-1-1-11-1-1-111-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-11111111111111111111-11111-1-1-1-111-1-1111111111111-1-1-1-1-1111-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-111-1
χ4111111111111111111111111111111111111111-1-11111111111111111111-1-1-111-1-1-1-111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1111-1-11
χ51111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-11-1-111-1-1-1-11-1-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-1-1-111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-111-1111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-1-1-111111-1-1-111-1-11111-1-1-11
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-11111-1-1111111-1-11111-1-1-1-11111-1-11-111-1-111-1-1-11-1-1-1-11111-1-1-11-11
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-11111-1-1-1-111-1-1-11-1111-1-1-1-111-1-111-1-1-1-111111-11-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-11-11-1-1-11111-1-111-1111-1-1-1-11111-1-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-11-1-111-1-1111-11-11111-1-1-1-1-1-111
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-1111111-1-1-1-11111-1-111-1-11-111-1-111-1-11-11-11111-1-111-1-11-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-11-1111-1-1-1-11111-1111-1-1-1-1-1-111-11
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χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-1-1-1-1-111-1-1-1-11111111111-11-1-111-1-111-11-1-1-1-1111111-11-1-1
χ17222222-1222-12-12-122-1-122-12-1-1-1-1-1222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-1-1-1-1-1-12002222-1-1-1-1-1-10022-1-1-1-1-1-1-1-122002000-1-1-1-100002000-1-100-1-1000000
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χ362222-122-1-1222222-1-1-122-12-1-1-1-122-1-1-122-1-1-1-1-2-200-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-10-2-2110000-2-200-2-2111111111100000-211000011110220000000000-1-10
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χ884-44-4-24-2-22-424-2-422-21-2022-21-1-12-22−2i32i300i3−i3i3−i300000023−23−23231-1-110−2i32i300i3−i3i3−i3000000000000000003i−3i3i−3i−333−300000000000000000000000000000000
χ894-44-4-24-2-22-424-2-422-21-2022-21-1-12-22−2i32i300i3−i3i3−i3000000−232323−231-1-110−2i32i300i3−i3i3−i300000000000000000−3i3i−3i3i3−3−3300000000000000000000000000000000
χ904-44-4-24-2-22-424-2-422-21-2022-21-1-12-222i3−2i300−i3i3−i3i300000023−23−23231-1-1102i3−2i300−i3i3−i3i300000000000000000−3i3i−3i3i−333−300000000000000000000000000000000
χ914-44-4-24-2-22-424-2-422-21-2022-21-1-12-222i3−2i300−i3i3−i3i3000000−232323−231-1-1102i3−2i300−i3i3−i3i3000000000000000003i−3i3i−3i3−3−3300000000000000000000000000000000
χ924-44-4-2-24-222-4-242-421-2-20-121-2222-2-1−2i32i300−2i32i3−2i32i300000000001-1-110i3−i300i3−i3i3−i3000000000000023−230000000000000000000000−333i−3i0000000000000000
χ934-44-4-2-24-222-4-242-421-2-20-121-2222-2-1−2i32i300−2i32i3−2i32i300000000001-1-110i3−i300i3−i3i3−i30000000000000−232300000000000000000000003−3−3i3i0000000000000000
χ944-44-4-2-24-222-4-242-421-2-20-121-2222-2-12i3−2i3002i3−2i32i3−2i300000000001-1-110−i3i300−i3i3−i3i3000000000000023−230000000000000000000000−33−3i3i0000000000000000
χ954-44-4-2-24-222-4-242-421-2-20-121-2222-2-12i3−2i3002i3−2i32i3−2i300000000001-1-110−i3i300−i3i3−i3i30000000000000−232300000000000000000000003−33i−3i0000000000000000
χ964-4-4444-2-4-4-4-2-424244-2-20-4-2-422-22240000000000004-4-22-22-22-220000000000000000000000004-40000-22-2200000000000000000000000000000000
χ974-4-4444-2-4-4-4-2-424244-2-20-4-2-422-2224000000000000-442-22-2-22-22000000000000000000000000-4400002-22-200000000000000000000000000000000
χ984-4-444-24-4-4242-4-2-44-24-202-22-4-4422-2000000000000000000-22-220000000000000000000000000000000000004i−4i000000000000000000−2i2i00000000
χ994-4-444-24-4-4242-4-2-44-24-202-22-4-4422-2000000000000000000-22-22000000000000000000000000000000000000−4i4i0000000000000000002i−2i00000000
χ1004-4-44-24422-44-4-44-4-2-2-24024222-2-4-4-20000000000004-44-44-4-22-22000000000000000000000000-220000-22-2200000000000000000000000000000000
χ1014-4-44-24422-44-4-44-4-2-2-24024222-2-4-4-2000000000000-44-44-44-22-220000000000000000000000002-200002-22-200000000000000000000000000000000
χ1024-4-44-24-222-4-2-4242-2-21-202-22-1-1122-200003i−3i−3i3i00004-4-22-221-11-1000003i−3i−3i3i000000000000000-223i−3i−3i3i1-11-100000000000000000000000000000000
χ1034-4-44-24-222-4-2-4242-2-21-202-22-1-1122-200003i−3i−3i3i0000-442-22-21-11-1000003i−3i−3i3i0000000000000002-2−3i3i3i−3i-11-1100000000000000000000000000000000
χ1044-4-44-24-222-4-2-4242-2-21-202-22-1-1122-20000−3i3i3i−3i00004-4-22-221-11-100000−3i3i3i−3i000000000000000-22−3i3i3i−3i1-11-100000000000000000000000000000000
χ1054-4-44-24-222-4-2-4242-2-21-202-22-1-1122-20000−3i3i3i−3i0000-442-22-21-11-100000−3i3i3i−3i0000000000000002-23i−3i−3i3i-11-1100000000000000000000000000000000
χ1068888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-422220000000000-1-1-1-1-42222-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ1078888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-20000000000-1-1-1-14-2-2-2-21111000000000000000000000000000000000000000000000000000000000
χ10888-8-8-4-484-4-4-84-84842-4-4024-24-44-44-200000000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000
χ10988-8-8-4-4-44-4-44444-4422202-2-2-22-22-2-20043−43−23−2323230000000000-1-111000−232333−3−3000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4-44-4-44444-4422202-2-2-22-22-2-200−43432323−23−230000000000-1-11100023−23−3−333000000000000000000000000000000000000000000000000000000000
χ1118-88-88-4-48-844-4-444-8-4-4204-2-4-444-2240000000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000
χ1128-88-8-4-4-4-4444-4-44442220-2-222-2-2-22-2−4i34i3002i3−2i32i3−2i30000000000-111-102i3−2i300−i3i3−i3i3000000000000000000000000000000000000000000000000000000000
χ1138-88-8-4-4-4-4444-4-44442220-2-222-2-2-22-24i3−4i300−2i32i3−2i32i30000000000-111-10−2i32i300i3−i3i3−i3000000000000000000000000000000000000000000000000000000000
χ1148-8-888-4-4-8-84-444-448-4-42042444-4-2-2-40000000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
χ1158-8-88-4-4844484-8-4-8-42-4-40-2-4-244-44420000000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-4444-444-44-42220-22-2-2-22-2-2200006i−6i−6i6i0000000000-11-1100000−3i3i3i−3i000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-4444-444-44-42220-22-2-2-22-2-220000−6i6i6i−6i0000000000-11-11000003i−3i−3i3i000000000000000000000000000000000000000000000000000000000

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