Finite Group Databasebeta

← Group #13168259

Character table — Group #13168259

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222444444444444444444444466668888888888889999121212121212121212121212121212121212121212121212121212121818181818182424242424242424242424243636363636365454545472727272
order122233344666666666333666666666121212121212121212124444366612121212121212122222444412121212121212121212121212121212121212121212121244666612121212121212121212121244441212444412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-111-1-111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111
χ51111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-111
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1
χ91111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-11-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111-11-111-1-111-1-11-11-1-1-111-1-11-11-1
χ101111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-11-111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-11-11-1-111-1-111-11-11-1-111-1-1-11-11
χ111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11-1-1111-1-1-1-1111-1-1111-1-1111-1-11
χ121111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-111-1-1-11111-1-1-111-111-1-111-111-1
χ131111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-11-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-111111-11-111-1-111-1-1-11-11-1-1-1-111-11-11
χ141111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-11-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-11111-11-11-1-111-1-1111-11-1-1-1-1-1111-11-1
χ151111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-11-1-1111-1-1-1-111-111-11111-1-1-111-1
χ161111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-111-1-1-11111-1-11-1-111111-1-11-1-11
χ17222222-122-12222-1-1222-1-1-1-12-1-122-1-12222-1-122220000-1-1-1-1-1-1-1-1-1-1-1-1222222220000-1-1-1-1-1-1-1-100000000000022-1-1-1-12222-1-1-1-1-1-1-1-10000-1-100000000
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χ22222222-1-2-2-12222-1-1222-1-1-1-12-1-122-1-1-2-2-2-211-2-2-2-20000-1-1-1-1111111112222-22-22000011-1-111-1-1000000000000-2-2-1-1-1-1-22-2211-1-111-1-100001100000000
χ23222222-1-2-2-12222-1-1222-1-1-1-12-1-122-1-1-2-2-2-211-2-2-2-20000-1-1-1-111111111-2-2-2-22-2-220000-1-11111-1-10000000000002211112-2-22-1-11111-1-10000-1-100000000
χ24222222-1-2-2-12222-1-1222-1-1-1-12-1-122-1-1-2-2-2-211-2-2-2-20000-1-1-1-111111111-2-2-2-2-222-2000011-1-1-1-111000000000000221111-222-211-1-1-1-1110000-1-100000000
χ2522222-122222-12-1222-1-12-12-1-12-1-1-12-122-1-122-1-1-1-12222-1-1-1-122-1-1-1-1-1-10000002222-1-10000222222-1-1-1-1-1-1-1-1-1-100000000-1-10000-1-1-1-1002200000000-1-1
χ2622222-122222-12-1222-1-12-12-1-12-1-1-12-122-1-122-1-1-1-12222-1-1-1-122-1-1-1-1-1-1000000-2-222-1-10000-2-2-2-222-1-1-1-1-1-1-1-1-1-100000000110000111100-2-20000000011
χ2722222-122222-12-1222-1-12-12-1-12-1-1-12-122-1-122-1-1-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-100000022-2-21100002222-2-2111111111100000000-1-10000-1-1-1-100-2-20000000011
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χ3122222-12-2-222-12-1222-1-12-12-1-12-1-1-12-1-2-211-2-21111-2-222-1-1-1-1-2-21111110000002-2-2-211000022-2-222-1-11111-1-1-1-100000000-110000-1-11100-22000000001-1
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χ362222-122222-12-1222-12-1-12-12-1-12-1-1-12-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-122-1-1-1-10000-2-20011-2-2-2-2-2-2000011-2-2111111110000001100111100002200000000-1-100
χ372222-122-2-22-12-1222-12-1-12-12-1-12-1-1-1211-2-2-2-2111122-2-2-1-1-1-111-2-2111100002-200-1-12222-2-2000011-2-2-1-1-1-11111000000-1100-1-11100002-200000000-1100
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χ8344-4-4-24-2-442-242-4-222-4-21-2-12-21-222-122-2-442-222-2-200001-1-11-112-2-1-11100000000000023−23−232300000000000000000000000000−333−3000000000000000000
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χ8744-4-4-2-24-44-4-2-2224-4221-2-2221-2-2-1-1222-22-2-44-1-11100001-1-112-22-2-1-1110000000000000000000000003i−3i3i−3i−3i3i−3i3i00000000000000000000000000000000
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χ894-44-444-2002-4-4442-2-4-44-2-222-4224-4-2-200000000000000-2-222000000004-44-4000000000000000000000000000000-22-2200000000000000000000000000
χ904-44-444-2002-4-4442-2-4-44-2-222-4224-4-2-200000000000000-2-22200000000-44-440000000000000000000000000000002-22-200000000000000000000000000
χ914-44-44-2400-4-424-2-44-42-24-2-422-42-224-20000000000004i−4i-2-22200000000000000000000000000004i−4i−2i2i0000−2i−2i2i2i00000000000000000000000000000000
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χ934-44-4-24400-42-4-24-442-4-2-242-422-4-22-240000000000004i−4i-2-2220000000000000000000000000000−2i2i4i−4i0000−2i−2i2i2i00000000000000000000000000000000
χ944-44-4-24400-42-4-24-442-4-2-242-422-4-22-24000000000000−4i4i-2-22200000000000000000000000000002i−2i−4i4i00002i2i−2i−2i00000000000000000000000000000000
χ954-44-4-2-2400-422-2-2-44221-2-222-1221-1-2-20000003i−3i3i−3i004i−4i11-1-100003i−3i3i−3i00000000000000000000−2i2i−2i2i3-3-33ii−i−i00000000000000000000000000000000
χ964-44-4-2-2400-422-2-2-44221-2-222-1221-1-2-20000003i−3i3i−3i00−4i4i11-1-100003i−3i3i−3i000000000000000000002i−2i2i−2i-333-3−i−iii00000000000000000000000000000000
χ974-44-4-2-2400-422-2-2-44221-2-222-1221-1-2-2000000−3i3i−3i3i004i−4i11-1-10000−3i3i−3i3i00000000000000000000−2i2i−2i2i-333-3ii−i−i00000000000000000000000000000000
χ984-44-4-2-2400-422-2-2-44221-2-222-1221-1-2-2000000−3i3i−3i3i00−4i4i11-1-10000−3i3i−3i3i000000000000000000002i−2i2i−2i3-3-33−i−iii00000000000000000000000000000000
χ994-4-4444-200-2-4-4-4-422444-2-2-2-2-422-442200000000000000-22-22000000004-4-44000000000000000000000000000000-222-200000000000000000000000000
χ1004-4-4444-200-2-4-4-4-422444-2-2-2-2-422-442200000000000000-22-2200000000-444-40000000000000000000000000000002-2-2200000000000000000000000000
χ1014-4-444-24004-42-42-4-44-2-24-24-22-422-2-4200000000004i−4i00-22-2200000000000000004i−4i−2i2i000000000000−2i−2i2i2i000000000000000000000000000000000000
χ1024-4-444-24004-42-42-4-44-2-24-24-22-422-2-420000000000−4i4i00-22-220000000000000000−4i4i2i−2i0000000000002i2i−2i−2i000000000000000000000000000000000000
χ1034-4-44-2440042-42-4-4-4-24-2-24-2422-42-22-400000000004i−4i00-22-220000000000000000−2i2i4i−4i000000000000−2i−2i2i2i000000000000000000000000000000000000
χ1044-4-44-2440042-42-4-4-4-24-2-24-2422-42-22-40000000000−4i4i00-22-2200000000000000002i−2i−4i4i0000000000002i2i−2i−2i000000000000000000000000000000000000
χ1054-4-44-2-240042222-4-4-2-21-2-2-2-2-122-11220000003i−3i−3i3i4i−4i001-11-100003i−3i−3i3i00000000−2i2i−2i2i000000000000ii−i−i-333-300000000000000000000000000000000
χ1064-4-44-2-240042222-4-4-2-21-2-2-2-2-122-11220000003i−3i−3i3i−4i4i001-11-100003i−3i−3i3i000000002i−2i2i−2i000000000000−i−iii3-3-3300000000000000000000000000000000
χ1074-4-44-2-240042222-4-4-2-21-2-2-2-2-122-1122000000−3i3i3i−3i4i−4i001-11-10000−3i3i3i−3i00000000−2i2i−2i2i000000000000ii−i−i3-3-3300000000000000000000000000000000
χ1084-4-44-2-240042222-4-4-2-21-2-2-2-2-122-1122000000−3i3i3i−3i−4i4i001-11-10000−3i3i3i−3i000000002i−2i2i−2i000000000000−i−iii-333-300000000000000000000000000000000
χ1098888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-422220000-1-1-1-12222-1-1-1-10000000000000000000000000000000000000000000000000000000000000000
χ1108888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-2-2-2-20000-1-1-1-1-2-2-2-211110000000000000000000000000000000000000000000000000000000000000000
χ11188-8-8-4-4-48-84-4-444-4444222-2-2222-2-2-2-2-44-44-4422-2-20000-111-12-22-2-1-1110000000000000000000000000000000000000000000000000000000000000000
χ11288-8-8-4-4-4-884-4-444-4444222-2-2222-2-2-2-24-44-44-4-2-2220000-111-1-22-2211-1-10000000000000000000000000000000000000000000000000000000000000000
χ1138-88-88-4-4004-848-44-4-84-4-424-244-2-44-420000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1148-88-8-48-40044-8-484-44-8-42-4-244-24-442-40000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1158-88-8-4-4-400444-4-44-444222-2-2-2-2-22-2220000006i−6i6i−6i0000-1-1110000−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000000000
χ1168-88-8-4-4-400444-4-44-444222-2-2-2-2-22-222000000−6i6i−6i6i0000-1-11100003i−3i3i−3i0000000000000000000000000000000000000000000000000000000000000000
χ1178-8-888-4-400-4-84-84448-4-4-42-4244-24-44-2000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1188-8-88-48-400-44-84-844-48-42-42-44-244-4-24000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1198-8-88-4-4-400-4444444-4-422222-2-2-2-22-2-20000006i−6i−6i6i0000-11-110000−3i3i3i−3i0000000000000000000000000000000000000000000000000000000000000000
χ1208-8-88-4-4-400-4444444-4-422222-2-2-2-22-2-2000000−6i6i6i−6i0000-11-1100003i−3i−3i3i0000000000000000000000000000000000000000000000000000000000000000

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