Finite Group Databasebeta

← Group #13155846

Character table — Group #13155846

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212121212121212121212121212181818181818242424242424242424242424363636727272727272108108
order1222333446666666663336666666661212121212121212121236661212121212121212222266666666882424242424242424242424242424242422666666666666666641212441212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-11-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11-1-11111
χ51111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-1-111-1-1
χ61111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-11-111-1-111
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1
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χ11222222-122222-1-12-1222-1-122-1-1-1-12-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000000022-1-1-1-12222-1-1-1-1-1-1-1-12-1-100000000
χ12222222-122222-1-12-1222-1-122-1-1-1-12-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-1-1-1-11111000000000000000000-2-2111122-2-2-1-1-1-11111-21100000000
χ13222222-122222-1-12-1222-1-122-1-1-1-12-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2221111-1-1-1-1000000000000000000-2-21111-2-2221111-1-1-1-1-21100000000
χ14222222-122222-1-12-1222-1-122-1-1-1-12-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000000022-1-1-1-1-2-2-2-2111111112-1-100000000
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χ1922222-122222-122-12-12-12-1-1-122-1-1-12-1-1222-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1220022220000222222-1-1-1-1-1-1-1-1-1-1-1-1000000-1-100-1-1-1-1000000020-1-10000
χ2022222-122222-122-12-12-12-1-1-122-1-1-12-1-1222-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1220022220000-2-2-2-2-2-2111111111111000000-1-100-1-1-1-10000000-20110000
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χ262222-12222-1-1222222-1-1-12-1-1-1-122-1-12222-1-1-12-1-1-1-1-1-1-1-1-122-1-1-1-100-2-20000-2-2-2-2-2-21111-2-2-2-2111111110000000011000011110000200-1-100
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χ422-2-2222-1-22-2-2-2112-1-222-1-1-2-211112-1-121-1222-2-2-2-2-111-11-11-111-1-1-22001-11-1i3−i3−i3i300000000000000000000−i3i3−i3i3-22001-11-1i3−i3−i3i30i3−i300000000
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χ824-44-4-2-24002-22-442-4-221-2-2-112-22-2-12200003i−3i00−3i3i1-11-10000−3i3i3i−3i000000000000006−6−66i6−i6−i6i6−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ1300000000000000000000000000000
χ834-44-4-2-24002-22-442-4-221-2-2-112-22-2-12200003i−3i00−3i3i1-11-10000−3i3i3i−3i00000000000000−666−6−i6i6i6−i6ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ1300000000000000000000000000000
χ844-44-4-2-24002-22-442-4-221-2-2-112-22-2-1220000−3i3i003i−3i1-11-100003i−3i−3i3i000000000000006−6−66−i6i6i6−i6ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ2300000000000000000000000000000
χ854-44-4-2-24002-22-442-4-221-2-2-112-22-2-1220000−3i3i003i−3i1-11-100003i−3i−3i3i00000000000000−666−6i6−i6−i6i6−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ2300000000000000000000000000000
χ864-4-444-244-4-4-42-4-4-2424-24-222-4-422-24-224-4-422-24-2-2-222-24-4-22-2-22200000000000000000000000000000000000000000000000000000000000
χ874-4-444-2-24-4-4-4222-2-224-2-212222-1-1-2-212-22-422-24-2-21-1-11-221-111-1-10000−2i32i32i3−2i300000000000000000000000000000000i3−i3−i3i3000000000000000
χ884-4-444-2-24-4-4-4222-2-224-2-212222-1-1-2-212-22-422-24-2-21-1-11-221-111-1-100002i3−2i3−2i32i300000000000000000000000000000000−i3i3i3−i3000000000000000
χ894-4-444-2-2-44-4-4222-2-224-2-212222-1-1-2-21-22-24-2-22-4221-1-112-2-11-1-1114-400-22-220000000000000000000000000000-22001-11-1000000000000000
χ904-4-444-2-2-44-4-4222-2-224-2-212222-1-1-2-21-22-24-2-22-4221-1-112-2-11-1-111-44002-22-200000000000000000000000000002-200-11-11000000000000000
χ914-4-44-244-4422-4-4-444-4-2-2-242222-4-4-2-244-44-2-2-2-4222-222-22-2-4422-2-200000000000000000000000000000000000000000000000000000000000
χ924-4-44-24-24-422-4224-2-4-2-21-222-1-122-21-2-4-222224-2-2-21-1-111-1-2211-1-1004-40000-22-2200000000000000000000000000-2200001-11-100000000000
χ934-4-44-24-24-422-4224-2-4-2-21-222-1-122-21-2-4-222224-2-2-21-1-111-1-2211-1-100-4400002-22-2000000000000000000000000002-20000-11-1100000000000
χ944-4-44-24-2-4422-4224-2-4-2-21-222-1-122-21-242-2-2-2-2-42221-1-11-112-2-1-11100000000−2i32i32i3−2i300000000000000000000000000000000i3−i3−i3i300000000000
χ954-4-44-24-2-4422-4224-2-4-2-21-222-1-122-21-242-2-2-2-2-42221-1-11-112-2-1-111000000002i3−2i3−2i32i300000000000000000000000000000000−i3i3i3−i300000000000
χ964-4-44-2-244-4222-4-4-242-21-2-2-1-122221-2-224-42-1-1-2-2111-1-11-22-2211-1-100000000000000−2i32i3−2i32i30000i3−i3i3−i3i3−i3i3−i300000000000000000000000000000
χ974-4-44-2-244-4222-4-4-242-21-2-2-1-122221-2-224-42-1-1-2-2111-1-11-22-2211-1-1000000000000002i3−2i32i3−2i30000−i3i3−i3i3−i3i3−i3i300000000000000000000000000000
χ984-4-44-2-24-44222-4-4-242-21-2-2-1-122221-2-2-2-44-21122-1-11-1-112-22-2-1-11100000000000000000023−2323−23−3−333−3−33300000000000000000000000000000
χ994-4-44-2-24-44222-4-4-242-21-2-2-1-122221-2-2-2-44-21122-1-11-1-112-22-2-1-111000000000000000000−2323−232333−3−333−3−300000000000000000000000000000
χ1008888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-422-4-422-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000000000
χ1018888-4-4-4-8-8-4-4-4-4-4-4-4-4-42222222222224444-2-244-2-2-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000000000
χ10288-8-88-4-4008-8-4-44444-8-4-42-44-442-244-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-48-400-448-44-84-84-42-4-442-2-444-24000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-400-44-4-4444442222-22-22-2-2-2-200006i−6i006i−6i-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-400-44-4-4444442222-22-22-2-2-2-20000−6i6i00−6i6i-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1068-88-88-4-400-8844-444-4-8-4-424-44-4-2244-200000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-48-4004-4-84-4-8484-42-44-4-224-44-2400000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-4004-444-444-44222-22-22-22-2-2-200006i−6i00−6i6i-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-4004-444-444-44222-22-22-22-2-2-20000−6i6i006i−6i-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-48-844444-4-44-4222-2-2-2-2-2-22224-444-2-2-4-422-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-8844444-4-44-4222-2-2-2-2-2-2222-44-4-42244-2-2-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.