Finite Group Databasebeta

← Group #13168670

Character table — Group #13168670

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size111122222222222222444444444444444444444466666688888888888812121212121212121212121212121212121212121212121818181818182424242424242424242424242424363636363636363636363654547272108
order12223334466666666633366666666612121212121212121212441212121236661212121212121212244446666666612121212121212121212444444121212121212121212121212121244412121212121212122212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-111-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1-11
χ51111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1111111-1-11
χ81111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-1
χ91111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-111-1-11111111111-1-11-11-11-111-1-111-1-1-11-111-1-111-1-1111-1-1
χ101111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-111-1-1111-1-1-1-1111-11-1-11111-1-1-1-1-111
χ111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-111-1-1-11111-1-111-1-1-111-1-111-1-11-11
χ121111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-11111111111-1-111-11-11-11-1-111-1-111-1-1111-1-1-1-11111-11-1
χ131111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-11-11111111111-1-1-1-1-1-1-1-111-1-1111-11-11-111-1-111-1-1-1-1111-1-1-1-111-1-1-111
χ141111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1111-1-1-1-11111-1-1-111-1-111111-1-1
χ151111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-111-111111111-1-111-1-1-1-1-1-1-1-111-1-11-1-111-1-1-11111-1-11-11-1-11111-1-111-11-1
χ161111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-1111111111-1-111-1-1-1-1-1-11111-1-1-11-11-11-1-111-1-111-11-111-1-111-1-1-1-11-11
χ17222222-12222-12-122-122-1-12-1-1-12-1-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12220022-1-1-1-1-1-1-1-1-1-122-1-1-1-1002222002200-1-1-1-100000000000-1-1-1-100000
χ18222222-12222-12-122-122-1-12-1-1-12-1-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-2-20022-1-1-1-1-1-1111122-1-1-1-100-2-2-2-200-2-200111100000000000111100000
χ19222222-12222-12-122-122-1-12-1-1-12-1-12-122-1-122-1-1-1-1-2-21111-1-1-1-122-1-1-1-1-1-1-22200-2-2111111-1-1-1-1-2-2111100-2-2-2-2002200-1-1-1-100000000000111100000
χ20222222-12222-12-122-122-1-12-1-1-12-1-12-122-1-122-1-1-1-1-2-21111-1-1-1-122-1-1-1-1-1-1-2-2-200-2-21111111111-2-2111100222200-2-200111100000000000-1-1-1-100000
χ21222222-1-2-222-12-122-122-1-12-1-1-12-1-12-1-2-211-2-2111122-1-1-1-1-1-1-1-1-2-2111111-22-200-2-2111111-1-11122-1-1-1-10022-2-2002-200-1-11100000000000-1-11100000
χ22222222-1-2-222-12-122-122-1-12-1-1-12-1-12-1-2-211-2-2111122-1-1-1-1-1-1-1-1-2-2111111-2-2200-2-211111111-1-122-1-1-1-100-2-22200-220011-1-10000000000011-1-100000
χ23222222-1-2-222-12-122-122-1-12-1-1-12-1-12-1-2-211-2-21111-2-21111-1-1-1-1-2-211111122-20022-1-1-1-1-1-1-1-111-2-2111100-2-222002-200-1-1110000000000011-1-100000
χ24222222-1-2-222-12-122-122-1-12-1-1-12-1-12-1-2-211-2-21111-2-21111-1-1-1-1-2-21111112-220022-1-1-1-1-1-111-1-1-2-211110022-2-200-220011-1-100000000000-1-11100000
χ2522222-1222-122-12222-1-12-1-12-1-1-12-1-122222-1-1-1-1-1-1222222-1-1-1-1-1-122-1-1-1-120022-1-122-1-1-1-10000-1-1-1-1-1-1000000-1-100220000-1-1-1-10220000000000-1-10
χ2622222-1222-122-12222-1-12-1-12-1-1-12-1-122222-1-1-1-1-1-1222222-1-1-1-1-1-122-1-1-1-1200-2-2-1-122-1-1-1-10000-1-1-1-1-1-10000001100-2-2000011110-2-20000000000110
χ2722222-1222-122-12222-1-12-1-12-1-1-12-1-122222-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-122-1-1-1-1-2002211-2-211110000111111000000-1-100220000-1-1-1-10-2-20000000000110
χ2822222-1222-122-12222-1-12-1-12-1-1-12-1-122222-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-122-1-1-1-1-200-2-211-2-2111100001111110000001100-2-2000011110220000000000-1-10
χ2922222-12-2-2-122-12222-1-12-1-12-1-1-12-1-12-2-2-2-2111111222222-1-1-1-111-2-21111-2002-211-2-211110000-1-1-1-1-1-1000000-11002-20000-1-11102-20000000000-110
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χ3122222-12-2-2-122-12222-1-12-1-12-1-1-12-1-12-2-2-2-2111111-2-2-2-2-2-2-1-1-1-111-2-211112002-2-1-122-1-1-1-10000111111000000-11002-20000-1-1110-2200000000001-10
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χ884-44-4-24400-42-44-4-224-4-2-242-24-422-4-220000000000000000-2-22200000000000000000000000000000004i−4i000000000000000000000−2i2i00000000000
χ894-44-4-24400-42-44-4-224-4-2-242-24-422-4-220000000000000000-2-2220000000000000000000000000000000−4i4i0000000000000000000002i−2i00000000000
χ904-4-444-244-42442-4-4-4-4-2-24-22-422-24-22-44-44-4-22-2-222000000-222-2-224-4-2-22200000000000000000000000000000000000000000000000000000000000
χ914-4-444-24-442442-4-4-4-4-2-24-22-422-24-22-4-44-442-222-2-2000000-222-22-2-4422-2-200000000000000000000000000000000000000000000000000000000000
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χ934-4-444-2-24-424-222-4-42-2-2-2122-1-1-2-21224-4-22-2211-1-1002i3−2i32i3−2i31-1-11-22-2211-1-100000002i3−2i3−i3−i3i3i3000000−i3i3−i3i3000000000000000000000000000000000000
χ944-4-444-2-2-4424-222-4-42-2-2-2122-1-1-2-2122-442-22-2-1-11100−2i32i3−2i32i31-1-112-22-2-1-11100000002i3−2i3−i3−i3i3i3000000i3−i3i3−i3000000000000000000000000000000000000
χ954-4-444-2-2-4424-222-4-42-2-2-2122-1-1-2-2122-442-22-2-1-111002i3−2i32i3−2i31-1-112-22-2-1-1110000000−2i32i3i3i3−i3−i3000000−i3i3−i3i3000000000000000000000000000000000000
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χ974-4-44-244-44-4-24-4-422-44-2-2422-4-4-2-24222-2-44-44-4-444000000-222-22-22-222-2-200000000000000000000000000000000000000000000000000000000000
χ984-4-44-24-24-4-4-2-2-422224-21-22-122-21-22-1-22-224-4-2-2220000001-1-11-221-111-1-1000000000000023−2323−23000000000000000000−33−3300000000000000000000
χ994-4-44-24-24-4-4-2-2-422224-21-22-122-21-22-1-22-224-4-2-2220000001-1-11-221-111-1-10000000000000−2323−23230000000000000000003−33−300000000000000000000
χ1004-4-44-24-2-44-4-2-2-422224-21-22-122-21-22-12-22-2-4422-2-20000001-1-112-2-11-1-111000000000000023−23−2323000000000000000000−333−300000000000000000000
χ1014-4-44-24-2-44-4-2-2-422224-21-22-122-21-22-12-22-2-4422-2-20000001-1-112-2-11-1-1110000000000000−232323−230000000000000000003−3−3300000000000000000000
χ1024-4-44-2-244-42-242-422-4-21-2-2-12221-2-2-12-224-4-22-2-2220000001-1-111-1-2211-1-10000000000000000000000000000000000000003i−3i3i−3i0000000000000000
χ1034-4-44-2-244-42-242-422-4-21-2-2-12221-2-2-12-224-4-22-2-2220000001-1-111-1-2211-1-1000000000000000000000000000000000000000−3i3i−3i3i0000000000000000
χ1044-4-44-2-24-442-242-422-4-21-2-2-12221-2-2-122-2-442-222-2-20000001-1-11-112-2-1-1110000000000000000000000000000000000000003i−3i−3i3i0000000000000000
χ1054-4-44-2-24-442-242-422-4-21-2-2-12221-2-2-122-2-442-222-2-20000001-1-11-112-2-1-111000000000000000000000000000000000000000−3i3i3i−3i0000000000000000
χ1068888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-42222000000-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000000000
χ1078888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-2-2-2-2000000-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000000000
χ10888-8-8-48-400844-8-44-44-8-42-4-4-24-44-244200000000000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
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χ11088-8-8-4-4-400-4444-44-4442222-2-22-2-2-2-220000006i−6i6i−6i000000-11-110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ11188-8-8-4-4-400-4444-44-4442222-2-22-2-2-2-22000000−6i6i−6i6i000000-11-1100003i−3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1128-88-8-48-400-84484-44-4-8-42-442-444-24-4-2000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1138-88-8-4-480044-8-4-8-44842-4-4-2-4-44-24424000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1148-88-8-4-4-400444-44-44-44222-222-2-2-2-22-20000006i−6i−6i6i000000-1-1110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1158-88-8-4-4-400444-44-44-44222-222-2-2-2-22-2000000−6i6i6i−6i000000-1-11100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-48-84-4-444444-4222-2-2-2-2222-2-2-44-44-4422-2-2000000-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-4-884-4-444444-4222-2-2-2-2222-2-24-44-44-4-2-222000000-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000000000

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