Finite Group Databasebeta

← Group #13168534

Character table — Group #13168534

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size111122222222222222444444444444444444444466666688888888888812121212121212121212121212121212121212121212121818181818182424242424242424242424242424363636363636363636363654547272108
order1222333446666666663336666666661212121212121212121244121212123666121212121212121222444666612121212121212121212121212124444446666661212121212121212244661212121212124412122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-11111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-1111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1-1-1-1-1-111-1
χ41111111111111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1-11
χ51111111111111111111111111111111111111111-1-1-1-1-1-111111111111111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-11111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1111111-1-11
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
χ91111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-11-111-1-111-1-1-1-11111-1-1-1-111-1-1111-111-1-11-11-111-1-1-11-1-1-11111-1-1111-1-1
χ101111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1111-1-111-1-1-1-11111-1-1-1-111-1-1-1-11-111-1-1-11-11-1-1111-1111-1-111-1-1-1-1-111
χ111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-11-1-1111-11-111-1-111-111-1-1-1-111-1-11-11
χ121111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-11111-1-1-1-1-1-11111-11-1-111-11-11-1-111-1-11-1-111-1-11111-11-1
χ131111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-111-111-1-1-1-11111-1-1-1-11111-1-111111-111-1-11-11-111-1-1-1-11-1-111-1-111-1-1-111
χ141111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-1111-1-1-1-11111-1-1-1-11111-1-111-1-11-111-1-1-11-11-1-11111-111-1-1-1-111111-1-1
χ151111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-11-1-1111-11-111-1-11-1111-1-111-1-111-11-1
χ161111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-11-1-111-1-11111-1-1-1-1111111-1-111-11-1-111-11-11-1-111-11-1-1-11111-1-1-1-11-11
χ17222222-122-12222-1-1222-1-1-1-1-12-1-122-12222-1-12222000000-1-1-1-1-1-1-1-1-1-1-1-122022222200000000000000000022-1-1-1-1-1-1-1-122-1-1-1-1200-1-1-1-1000000000
χ18222222-122-12222-1-1222-1-1-1-1-12-1-122-12222-1-12222000000-1-1-1-1-1-1-1-1-1-1-1-1220-2-22222000000000000000000-2-2-1-1-1-1-1-111-2-21111-2001111000000000
χ19222222-122-12222-1-1222-1-1-1-1-12-1-122-12222-1-12222000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2022-2-2-2-2000000000000000000-2-2111111-1-122-1-1-1-1-2001111000000000
χ20222222-122-12222-1-1222-1-1-1-1-12-1-122-12222-1-12222000000-1-1-1-1-1-1-1-1-1-1-1-1-2-20-2-2-2-2-2-20000000000000000002211111111-2-21111200-1-1-1-1000000000
χ21222222-1-2-2-12222-1-1222-1-1-1-1-12-1-122-1-2-2-2-211-2-2-2-2000000-1-1-1-1111111112-202-222-2-200000000000000000022-11-1-111-112-2-1-111-20011-1-1000000000
χ22222222-1-2-2-12222-1-1222-1-1-1-1-12-1-122-1-2-2-2-211-2-2-2-2000000-1-1-1-1111111112-20-2222-2-2000000000000000000-2-2-11-1-1111-1-2211-1-1200-1-111000000000
χ23222222-1-2-2-12222-1-1222-1-1-1-1-12-1-122-1-2-2-2-211-2-2-2-2000000-1-1-1-111111111-2202-2-2-222000000000000000000-2-21-111-1-1-112-2-1-111200-1-111000000000
χ24222222-1-2-2-12222-1-1222-1-1-1-1-12-1-122-1-2-2-2-211-2-2-2-2000000-1-1-1-111111111-220-22-2-222000000000000000000221-111-1-11-1-2211-1-1-20011-1-1000000000
χ2522222-122222-12-122-12-12-12-1-1-12-1-1-1222-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-122200-1-1-1-122-1-122-1-1-1-1-1-1-1-122220022-1-1-1-1000000000000000-1-1-1-100000
χ2622222-122222-12-122-12-12-12-1-1-12-1-1-1222-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2200111122-1-122-1-1-1-1-1-1-1-1-2-2-2-200-2-21111000000000000000111100000
χ2722222-122222-12-122-12-12-12-1-1-12-1-1-1222-1-122-1-1-1-1-2-21111-1-1-1-122-1-1-1-1-1-122-200-1-1-1-1-2-211-2-211111111-2-2-2-20022-1-1-1-1000000000000000111100000
χ2822222-122222-12-122-12-12-12-1-1-12-1-1-1222-1-122-1-1-1-1-2-21111-1-1-1-122-1-1-1-1-1-1-2-2-2001111-2-211-2-211111111222200-2-21111000000000000000-1-1-1-100000
χ2922222-12-2-222-12-122-12-12-12-1-1-12-1-1-12-2-211-2-2111122-1-1-1-1-1-1-1-1-2-21111112-2-200-1-1112211-2-2-1-1-1-1111122-2-2002-2-1-111000000000000000-1-11100000
χ3022222-12-2-222-12-122-12-12-12-1-1-12-1-1-12-2-211-2-2111122-1-1-1-1-1-1-1-1-2-2111111-22-20011-1-12211-2-2-1-1-1-11111-2-22200-2211-1-100000000000000011-1-100000
χ3122222-12-2-222-12-122-12-12-12-1-1-12-1-1-12-2-211-2-21111-2-21111-1-1-1-1-2-21111112-2200-1-111-2-2-1-1221111-1-1-1-1-2-222002-2-1-11100000000000000011-1-100000
χ3222222-12-2-222-12-122-12-12-12-1-1-12-1-1-12-2-211-2-21111-2-21111-1-1-1-1-2-2111111-2220011-1-1-2-2-1-1221111-1-1-1-122-2-200-2211-1-1000000000000000-1-11100000
χ332222-122222-12-12222-1-1-12-122-1-12-1-1-1-1-12222-1-1-1-1222222-1-1-1-1-1-122-1-1-1-1002220000-1-122-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1-1-10220000000000-1-10
χ342222-122222-12-12222-1-1-12-122-1-12-1-1-1-1-12222-1-1-1-1222222-1-1-1-1-1-122-1-1-1-1002-2-20000-1-122-1-1-1-1-1-1-1-1-1-1000000000000-2-21111110-2-20000000000110
χ352222-122222-12-12222-1-1-12-122-1-12-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-122-1-1-1-100-222000011-2-2111111111100000000000022-1-1-1-1-1-10-2-20000000000110
χ362222-122222-12-12222-1-1-12-122-1-12-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-122-1-1-1-100-2-2-2000011-2-21111111111000000000000-2-21111110220000000000-1-10
χ372222-122-2-22-12-12222-1-1-12-122-1-12-1-1-111-2-2-2-21111222222-1-1-1-111-2-2111100-22-20000-1-1-2-211-1-1-1-111110000000000002-2-11-1-11102-20000000000-110
χ382222-122-2-22-12-12222-1-1-12-122-1-12-1-1-111-2-2-2-21111222222-1-1-1-111-2-2111100-2-220000-1-1-2-211-1-1-1-11111000000000000-221-111-1-10-2200000000001-10
χ392222-122-2-22-12-12222-1-1-12-122-1-12-1-1-111-2-2-2-21111-2-2-2-2-2-2-1-1-1-111-2-211110022-200001122-1-11111-1-1-1-10000000000002-2-11-1-1110-2200000000001-10
χ402222-122-2-22-12-12222-1-1-12-122-1-12-1-1-111-2-2-2-21111-2-2-2-2-2-2-1-1-1-111-2-21111002-2200001122-1-11111-1-1-1-1000000000000-221-111-1-102-20000000000-110
χ4122-2-2222002-2-22-2-2-22-222222-2-2-2-22-2-200000000002-222-2-222-2-2000000000000000002-2000022-2-2000000002i−2i00000000000000000002i−2i00002i−2i000
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χ4422-2-2222002-2-22-2-2-22-222222-2-2-2-22-2-20000000000-22-2-22222-2-200000000000000000-220000-2-22200000000−2i2i0000000000000000000−2i2i00002i−2i000
χ452-2-222222-2-222-2-2-22-2-2222-2-2-2222-2-2-22-22-22-222-2-20000002-2-222-22-222-2-2000000000000000000000002i−2i2i−2i000000000000000000000002i−2i2i−2i00000
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χ482-2-22222-22-222-2-2-22-2-2222-2-2-2222-2-2-2-22-22-22-2-2220000002-2-22-22-22-2-22200000000000000000000000−2i2i2i−2i00000000000000000000000−2i2i2i−2i00000
χ492-2-222-122-2-22-1-21-221-2-12-1-211-12-111-22-2-112-2-1-111003−33−3-111-12-2-11-1-11100000−i3i3−i3i3003−3003−33−333−3−32i−2i2i−2i0000−i3i3−i3i3000000000000000−ii−ii00000
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χ874-44-4-2-2400-4222-24-42-21-2-222-2-122-11-20000003i−3i−3i3i00−232323−231-11-100003i−3i−3i3i00000000000002i3−2i33−3−33−i3i3i3−i3000000000000000000000000000000000000
χ884-44-4-2-2400-4222-24-42-21-2-222-2-122-11-2000000−3i3i3i−3i0023−23−23231-11-10000−3i3i3i−3i00000000000002i3−2i3−333−3−i3i3i3−i3000000000000000000000000000000000000
χ894-44-4-2-2400-4222-24-42-21-2-222-2-122-11-2000000−3i3i3i−3i00−232323−231-11-10000−3i3i3i−3i0000000000000−2i32i33−3−33i3−i3−i3i3000000000000000000000000000000000000
χ904-4-4444-24-4244-4-42-2-4-44-2-22224-2-2-4-424-44-4-2244-4-4000000-222-2-22-22-2-22200000000000000000000000000000000000000000000000000000000000
χ914-4-4444-2-44244-4-42-2-4-44-2-22224-2-2-4-42-44-442-2-4-444000000-222-22-22-222-2-200000000000000000000000000000000000000000000000000000000000
χ924-4-444-2-24-424-2-422-22-4-2-212-1-1-2-212224-4-22-22-2-2220000001-1-11-221-111-1-100000−2i32i3−2i32i30000000000000000000000i3−i3i3−i3000000000000000000000000
χ934-4-444-2-24-424-2-422-22-4-2-212-1-1-2-212224-4-22-22-2-2220000001-1-11-221-111-1-1000002i3−2i32i3−2i30000000000000000000000−i3i3−i3i3000000000000000000000000
χ944-4-444-2-2-4424-2-422-22-4-2-212-1-1-2-21222-442-22-222-2-20000001-1-112-2-11-1-11100000−2i32i32i3−2i30000000000000000000000i3−i3−i3i3000000000000000000000000
χ954-4-444-2-2-4424-2-422-22-4-2-212-1-1-2-21222-442-22-222-2-20000001-1-112-2-11-1-111000002i3−2i3−2i32i30000000000000000000000−i3i3i3−i3000000000000000000000000
χ964-4-44-2444-4-4-242-4-44-42-2-242-4-4-2-24222-224-44-4-2-222000000-222-2-224-4-2-22200000000000000000000000000000000000000000000000000000000000
χ974-4-44-244-44-4-242-4-44-42-2-242-4-4-2-242222-2-44-4422-2-2000000-222-22-2-4422-2-200000000000000000000000000000000000000000000000000000000000
χ984-4-44-24-24-42-242-42-2-42-21-2-122-21-222-1-224-4-22-2-2220000001-1-111-1-2211-1-10000000000000000000000000000000000000003i−3i3i−3i0000000000000000
χ994-4-44-24-24-42-242-42-2-42-21-2-122-21-222-1-224-4-22-2-2220000001-1-111-1-2211-1-1000000000000000000000000000000000000000−3i3i−3i3i0000000000000000
χ1004-4-44-24-2-442-242-42-2-42-21-2-122-21-222-12-2-442-222-2-20000001-1-11-112-2-1-1110000000000000000000000000000000000000003i−3i−3i3i0000000000000000
χ1014-4-44-24-2-442-242-42-2-42-21-2-122-21-222-12-2-442-222-2-20000001-1-11-112-2-1-111000000000000000000000000000000000000000−3i3i3i−3i0000000000000000
χ1024-4-44-2-244-4-4-2-222-44221-2-22221-2-2-1-12-22-224-411-1-10023−2323−231-1-11-22-2211-1-10000000000023−2300−33−33−3−333000000000000000000000000000000000000
χ1034-4-44-2-244-4-4-2-222-44221-2-22221-2-2-1-12-22-224-411-1-100−2323−23231-1-11-22-2211-1-100000000000−2323003−33−333−3−3000000000000000000000000000000000000
χ1044-4-44-2-24-44-4-2-222-44221-2-22221-2-2-1-122-22-2-44-1-1110023−2323−231-1-112-22-2-1-11100000000000−232300−33−3333−3−3000000000000000000000000000000000000
χ1054-4-44-2-24-44-4-2-222-44221-2-22221-2-2-1-122-22-2-44-1-11100−2323−23231-1-112-22-2-1-1110000000000023−23003−33−3−3−333000000000000000000000000000000000000
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
χ10888-8-88-4-400-4-848444-4-8-4-42-42-244-2-444000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ10988-8-8-48-400-44-8-4-84484-42-42-444-24-44-2000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4-400-444-4444-4422222-2-2-2-22-2-20000006i−6i6i−6i000000-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ11188-8-8-4-4-400-444-4444-4422222-2-2-2-22-2-2000000−6i6i−6i6i000000-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1128-88-88-4-4004-84-8-4-4448-4-424-2244-24-4-400000000000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1138-88-8-48-40044-848-44-8-4-42-4-24-44-244-4200000000000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1148-88-8-4-4-4004444-4-444-4222-2-22-2-2-2-2220000006i−6i−6i6i000000-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1158-88-8-4-4-4004444-4-444-4222-2-22-2-2-2-222000000−6i6i6i−6i000000-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-48-84-4-4444-444222-2-2-2222-2-2-2-44-44-4422-2-2000000-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-4-884-4-4444-444222-2-2-2222-2-2-24-44-44-4-2-222000000-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000000000

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