Finite Group Databasebeta

← Group #13155949

Character table — Group #13155949

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size11222222222222244444444444444444444444888888888888121212121212121212121212121212121212242424242424242424242424242424242424363636363636727272727272216
order12233344666121212123336666666612121212121212121212121236666612121212121244121212121212121212121212121212128824242424242424242424242424242424222244666612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111-111-1-1111111-1-1-1-1-1-11-1-1-11-11-1-1-11-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-11-1-111-1-1-1-1-1-1111111-11-1-1-11-11-1-1-11-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11
χ511111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-111-1-1-1
χ611111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1111111-1-1-1-1-1-1-11-1-1-11-11-1-1-111
χ711111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-11111111-1-1-11-11-1-1-11-11
χ811111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1
χ9222222-2-2222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000000000002-200002-2000
χ10222222-2-2222-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-200000000000000000000000000000000000000-220000-22000
χ1122222-122-12222222-1-1-12-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000222222-1-1-1-1-1-1-1-1-1-1-1-100220000-1-1000
χ1222222-122-12222222-1-1-12-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002-222-2-2-1-1-1-1-1-111111100-2-2000011000
χ1322222-122-12222222-1-1-12-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-22-2-222111111-1-1-1-1-1-100-2-2000011000
χ1422222-122-12222222-1-1-12-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2-2-2-2-211111111111100220000-1-1000
χ1522222-1-2-2-122-2-2-2-22-1-1-12-1-12222-2-2-2-2-2-2111111-1-1-1-1-1-1111111000000000000000000000000333−3−3−3333−3−3−3002-20000-11000
χ1622222-1-2-2-122-2-2-2-22-1-1-12-1-12222-2-2-2-2-2-2111111-1-1-1-1-1-1111111000000000000000000000000333−3−3−3−3−3−333300-2200001-1000
χ1722222-1-2-2-122-2-2-2-22-1-1-12-1-12222-2-2-2-2-2-2111111-1-1-1-1-1-1111111000000000000000000000000−3−3−3333333−3−3−300-2200001-1000
χ1822222-1-2-2-122-2-2-2-22-1-1-12-1-12222-2-2-2-2-2-2111111-1-1-1-1-1-1111111000000000000000000000000−3−3−3333−3−3−3333002-20000-11000
χ192222-122222-122-1-1-12-12-12-12-1-1-12-1-1-1-1-12222-1-1-12-1-1-1-12-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-10200-1-10000002-1-12-1-10200020-1000-10
χ202222-122222-122-1-1-12-12-12-12-1-1-12-1-1-1-1-12222-1-1-12-1-1-1-12-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-10-20011000000-211-2110-2000-20100010
χ212222-122222-122-1-1-12-12-12-12-1-1-12-1-1-1-1-12222-1-1-12-1-1-1-12-1-1-1-1-1-2-2-2-2-2-21111111111110200-1-10000002-1-12-1-10-2000-20100010
χ222222-122222-122-1-1-12-12-12-12-1-1-12-1-1-1-1-12222-1-1-12-1-1-1-12-1-1-1-1-1-2-2-2-2-2-21111111111110-20011000000-211-2110200020-1000-10
χ23222-122222-12-1-122-1-122-1-12-12-1-1-12-1-1-1-122-1-122-1-12-1-1-1-12-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-120-1-1002-1-12-1-1000000200020-1000-100
χ24222-122222-12-1-122-1-122-1-12-12-1-1-12-1-1-1-122-1-122-1-12-1-1-1-12-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-201100-211-211000000-2000-201000100
χ25222-122222-12-1-122-1-122-1-12-12-1-1-12-1-1-1-122-1-122-1-12-1-1-1-12-1-1-1-1-2-21111-2-2-2-21111111120-1-1002-1-12-1-1000000-2000-201000100
χ26222-122222-12-1-122-1-122-1-12-12-1-1-12-1-1-1-122-1-122-1-12-1-1-1-12-1-1-1-1-2-21111-2-2-2-211111111-201100-211-211000000200020-1000-100
χ2722-22222-222222-2-2222-2222-2-2-2-2-2222-2-22-222-2-22-2-2-2-22-2222-2-200000000000000000000000000000000000002000-202000-20
χ2822-22222-222222-2-2222-2222-2-2-2-2-2222-2-22-222-2-22-2-2-2-22-2222-2-20000000000000000000000000000000000000-200020-200020
χ2922-2222-22222-2-222222-2222-2-2-2-22-2-2-222-22-2-2222-2-2-2-222-2-2-2220000000000000000000000000000000000002000-202000-200
χ3022-2222-22222-2-222222-2222-2-2-2-22-2-2-222-22-2-2222-2-2-2-222-2-2-222000000000000000000000000000000000000-200020-2000200
χ3122-22-122-222-12211-12-1-2-12-1-2111-2-1-1-1112-22211-1-2111-1-2-1-1-11100000033−3−33333−3−3−3−300003−300000003−303−302000-20-100010
χ3222-22-122-222-12211-12-1-2-12-1-2111-2-1-1-1112-22211-1-2111-1-2-1-1-11100000033−3−33333−3−3−3−30000−330000000−330−330-2000201000-10
χ3322-22-122-222-12211-12-1-2-12-1-2111-2-1-1-1112-22211-1-2111-1-2-1-1-111000000−3−333−3−3−3−3333300003−300000003−303−30-2000201000-10
χ3422-22-122-222-12211-12-1-2-12-1-2111-2-1-1-1112-22211-1-2111-1-2-1-1-111000000−3−333−3−3−3−333330000−330000000−330−3302000-20-100010
χ3522-2-122-222-121122-1-12-2-1-121-211-1-211-1-1-221122-11-211-1-1-211-1-10033−3−3000033−3−333−3−3003−30003−303−30000002000-20-1000100
χ3622-2-122-222-121122-1-12-2-1-121-211-1-211-1-1-221122-11-211-1-1-211-1-10033−3−3000033−3−333−3−300−33000−330−33000000-2000201000-100
χ3722-2-122-222-121122-1-12-2-1-121-211-1-211-1-1-221122-11-211-1-1-211-1-100−3−3330000−3−333−3−333003−30003−303−3000000-2000201000-100
χ3822-2-122-222-121122-1-12-2-1-121-211-1-211-1-1-221122-11-211-1-1-211-1-100−3−3330000−3−333−3−33300−33000−330−330000002000-20-1000100
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χ404444-2-244-24-244-2-2-2-21-2-2-214-2-2-24-2-2-2-2-2-2-2-2-2111-21111-2111110000000000000000000400-2-2000000-211-2110000000000000
χ414444-2-244-24-244-2-2-2-21-2-2-214-2-2-24-2-2-2-2-2-2-2-2-2111-21111-2111110000000000000000000-400220000002-1-12-1-10000000000000
χ424444-2-2-4-4-24-2-4-422-2-21-2-2-214-2-2-2-4222222222-1-11-211112-1-1-1-1-100000000000000000000000000000023−3−3−23330000000000000
χ434444-2-2-4-4-24-2-4-422-2-21-2-2-214-2-2-2-4222222222-1-11-211112-1-1-1-1-1000000000000000000000000000000−233323−3−30000000000000
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χ45444-24-244-2-24-2-244-21-2-2-21-2-24-2-2-24-2-2-2-2-2-211-2-211-21111-2111100000000000000000040-2-200-211-2110000000000000000000
χ46444-24-244-2-24-2-244-21-2-2-21-2-24-2-2-24-2-2-2-2-2-211-2-211-21111-21111000000000000000000-4022002-1-12-1-10000000000000000000
χ47444-24-2-4-4-2-2422-4-4-21-2-2-21-2-24-2-22-4222222-1-12211-2111-12-1-1-1-100000000000000000000000023−3−3−23330000000000000000000
χ48444-24-2-4-4-2-2422-4-4-21-2-2-21-2-24-2-22-4222222-1-12211-2111-12-1-1-1-1000000000000000000000000−233323−3−30000000000000000000
χ49444-2-24444-2-2-2-2-2-21-2-241-2-2-2-211-2-2111144-2-2-2-21-2-2111-2-2111144-2-2-2-2-2-2-2-2111111110000000000000000000000000000000
χ50444-2-24444-2-2-2-2-2-21-2-241-2-2-2-211-2-2111144-2-2-2-21-2-2111-2-21111-4-422222222-1-1-1-1-1-1-1-10000000000000000000000000000000
χ51444-2-24-4-44-2-222221-2-241-2-2-2-21122-1-1-1-1-4-422221-2-211122-1-1-1-1000000000033-3-3-3-3330000000000000000000000000000000
χ52444-2-24-4-44-2-222221-2-241-2-2-2-21122-1-1-1-1-4-422221-2-211122-1-1-1-10000000000-3-33333-3-30000000000000000000000000000000
χ5344-444-24-4-24444-4-44-2-224-2-2-4-4-4-4-4444-4-4-22-2-222-22222-22-2-2-2220000000000000000000000000000000000000000000000000
χ5444-444-2-44-244-4-4444-2-224-2-2-4-4-4-44-4-4-4442-222-2-2-22222-2-2222-2-20000000000000000000000000000000000000000000000000
χ5544-44-24-4444-2-4-4-2-2-24-2-4-24-2-42224222-2-2-44-4-4-2-2-2-4222-24222-2-20000000000000000000000000000000000000000000000000
χ5644-44-2-24-4-24-24422-2-212-2-21-4222-4-2-2-222-22-2-2-1-112-1-1-112111-1-1000000000000000000000023−230000000−330−330000000000000
χ5744-44-2-24-4-24-24422-2-212-2-21-4222-4-2-2-222-22-2-2-1-112-1-1-112111-1-10000000000000000000000−232300000003−303−30000000000000
χ5844-44-2-2-44-24-2-4-4-2-2-2-212-2-21-42224222-2-22-2221112-1-1-11-2-1-1-11100000000000000000000000000000003-30-330000000000000
χ5944-44-2-2-44-24-2-4-4-2-2-2-212-2-21-42224222-2-22-2221112-1-1-11-2-1-1-1110000000000000000000000000000000-3303-30000000000000
χ6044-4-2444-44-24-2-2-4-4-2-24-4-2-242-42224-2-2224-4-2-2-4-4-22-422-224-2-2220000000000000000000000000000000000000000000000000
χ6144-4-24-24-4-2-24-2-2-4-4-21-22-21-22-42224-2-222-2211221-12-1-11-1-211-1-100000000000000000000000003-30-330000000000000000000
χ6244-4-24-24-4-2-24-2-2-4-4-21-22-21-22-42224-2-222-2211221-12-1-11-1-211-1-10000000000000000000000000-3303-30000000000000000000
χ6344-4-24-2-44-2-242244-21-22-21-22-422-2-422-2-22-2-1-1-2-21-12-1-1112-1-1110000000000000000000023−23000−330−330000000000000000000
χ6444-4-24-2-44-2-242244-21-22-21-22-422-2-422-2-22-2-1-1-2-21-12-1-1112-1-11100000000000000000000−23230003−303−30000000000000000000
χ6544-4-2-244-44-2-2-2-2221-2-2-41-2-222-1-12-211-1-14-4-2-222122-1-112-211-1-10000002323−23−23−3−3−3−333330000000000000000000000000000000
χ6644-4-2-244-44-2-2-2-2221-2-2-41-2-222-1-12-211-1-14-4-2-222122-1-112-211-1-1000000−23−2323233333−3−3−3−30000000000000000000000000000000
χ6744-4-2-24-444-2-222-2-21-2-2-41-2-222-1-1-22-1-111-4422-2-2122-1-11-22-1-111002323−23−230000−3−333−3−3330000000000000000000000000000000
χ6844-4-2-24-444-2-222-2-21-2-2-41-2-222-1-1-22-1-111-4422-2-2122-1-11-22-1-11100−23−232323000033−3−333−3−30000000000000000000000000000000
χ694-4044400-4-4-400004440-4-4-4000000000000000040000-40000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000
χ704-4044400-4-4-400004440-4-4-4000000000000000040000-4000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000
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χ814-40-2-2400-42223−23−23231-2-20-12200-3300−333−30023−23−2323100-33-100−333−32i−2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ii−ζ2−2ζ7+ζ10−2ζ11ζ2+2ζ7−ζ10+2ζ11ζ2−2ζ7−ζ10−2ζ11−ζ2+2ζ7+ζ10+2ζ11−ii0000000000000000000000000000000
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χ844-40-2-2400-422−232323−231-2-20-12200-33003−3−3300−232323−23100-33-1003−3−33−2i2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11i−i−ζ2+2ζ7+ζ10+2ζ11ζ2−2ζ7−ζ10−2ζ11ζ2+2ζ7−ζ10+2ζ11−ζ2−2ζ7+ζ10−2ζ11i−i0000000000000000000000000000000
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χ864-40-2-2400-422−2323−23231-2-20-122003-3003−33−300−2323−23231003-3-1003−33−3−2i2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+2ζ7−ζ10+2ζ11−ζ2−2ζ7+ζ10−2ζ11i−ii−i−ζ2+2ζ7+ζ10+2ζ11ζ2−2ζ7−ζ10−2ζ110000000000000000000000000000000
χ87888-4-4-488-4-4-4-4-4-4-4222-4222-4-422-4-42222-4-42222-122-1-1-122-1-1-1-10000000000000000000000000000000000000000000000000
χ88888-4-4-4-8-8-4-4-44444222-4222-4-42244-2-2-2-244-2-2-2-2-122-1-1-1-2-211110000000000000000000000000000000000000000000000000
χ8988-8-4-4-48-8-4-4-4-4-444222422244-2-24-422-2-2-4422-2-2-1-2-211-1-22-1-1110000000000000000000000000000000000000000000000000
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χ918-8088-4004-8-800008-4-40-8440000000000000000-4000040000000000000000000000000000000000000000000000000000000
χ928-808-4-4004-840043−43-4-42044-20000000043−430000−232320000-20000−23230000000000000000000000000000000000000000000000000
χ938-808-4-4004-8400−4343-4-42044-200000000−4343000023−2320000-2000023−230000000000000000000000000000000000000000000000000
χ948-80-48-40044-843−4300-42-404-2400000043−430000−23230020000-200−2323000000000000000000000000000000000000000000000000000
χ958-80-48-40044-8−434300-42-404-24000000−4343000023−230020000-20023−23000000000000000000000000000000000000000000000000000
χ968-80-4-4-40044443−4343−432220-2-2-2006-600−2323−232300−2323−2323-100-331003−33−30000000000000000000000000000000000000000000000000
χ978-80-4-4-40044443−43−43432220-2-2-200-6600−232323−2300−232323−23-1003-31003−3−330000000000000000000000000000000000000000000000000
χ988-80-4-4-400444−434343−432220-2-2-200-660023−23−23230023−23−2323-1003-3100−333−30000000000000000000000000000000000000000000000000
χ998-80-4-4-400444−4343−43432220-2-2-2006-60023−2323−230023−2323−23-100-33100−33−330000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.