Finite Group Databasebeta

← Group #13170663

Character table — Group #13170663

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size1122222222222224444444444444444444444466888888888888121212121212121212121212121212121212121212121212121212121218181818242424242424242424242424363636363636363672727272108108
order12233344666661212333666666666121212121212121212121288366661212121212121222246666668121224242424242424242424242424242424224466666666612121222246612126661288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-11111-1-11-1-11111111111111111-1-1-1-1-111-1-11111-1-1-111-1-1-1-1-1-1-111-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-111-1-1-1-1111111111111111111111-1-1-1-11-1-111-1-1-1-1111-1-111-1-1-1-11-1-11-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111111111111-1-11111111111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111111111111111-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111-1-1-1-11-1-1111
χ711111111111111111111111111111111111111-1-1111111111111-1-111-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111111-1-1-1-1-1-1-111-111
χ811111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911-1111-11-1-1111-1-1111-1-1-1-1-1-1111-11-1-1-1-1-11111111-1-1-111-1111-1-11-11-111-1-111-1-1-111111111-1-1-1-1-1-1-1-11-11-111-11111-1-1-1-1-11-11-11-11-111-1-11-1
χ1011-1111-11-1-1111-1-1111-1-1-1-1-1-1111-11-1-1-1-1-11111111-1-1-111-1111-1-11-1-1111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-11-1-1-111-1-11111-1-11-11-11-11-11-11
χ1111-1111-11-1-1111-1-1111-1-1-1-1-1-1111-11-1-1-1-1-11111111-1-1-111-1111-1-1-111-1-1-11111-1-1-111111111-1-1-1-1-1-1-1-1-11-111-1111-1-111-1-1-1-111-1-11-111-11-1-11
χ1211-1111-11-1-1111-1-1111-1-1-1-1-1-1111-11-1-1-1-1-11111111-1-1-111-1111-1-1-11-11-1-111-1-1-11111111111-1-1-1-1-1-1-1-11-11-1-1-11-1-1-1-111111-11-111-11-1-1-1111-1
χ1311-1111-11-1-1111-1-1111-1-1-1-1-1-1111-11-1-1-1-1-11111-1-11-1-1-111-1111-1-11-11-111-1-1111-1-1-1-1-1-1-1-1-1-1111111111-11-111-11111-1-1-1-1-1-11-111-11-1-1-111-11
χ1411-1111-11-1-1111-1-1111-1-1-1-1-1-1111-11-1-1-1-1-11111-1-11-1-1-111-1111-1-11-1-1111-1-1-1-1111-1-1-1-1-1-1-1-111111111-11-11-11-1-1-111-1-1111-111-1-11-111-11-11-1
χ1511-1111-11-1-1111-1-1111-1-1-1-1-1-1111-11-1-1-1-1-11111-1-11-1-1-111-1111-1-1-111-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-11-111-1111-1-111-1-1-11-1-11-11-11-11-111-1
χ1611-1111-11-1-1111-1-1111-1-1-1-1-1-1111-11-1-1-1-1-11111-1-11-1-1-111-1111-1-1-11-11-1-111-1-1111-1-1-1-1-1-1-1-1111111111-11-1-1-11-1-1-1-1111111-11-11-11-111-1-1-11
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χ262222-12222222-1222-1-12-122-1-12-1-12-1-122-1-1222200-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111101100000000000000002222-2-2-2111111-2110000-1-1-1-1000000
χ272222-12-2-22222-1-2-22-1-12-122-1-12-1-1-211-2-211-2-2-2-200-1-1-1-1-111111110000−i3i3−i3i3−i3i30−i3i300000000000000002-2-22000−i3i3−i3i3−i3i30−i3i30000-111-1000000
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χ292222-12-2-22222-1-2-22-1-12-122-1-12-1-1-211-2-211-2-2-2-200-1-1-1-1-111111110000i3−i3i3−i3−i3i30−i3i30000000000000000-222-2000−i3i3i3−i3i3−i30−i3i300001-1-11000000
χ302222-12-2-22222-1-2-22-1-12-122-1-12-1-1-211-2-211-2-2-2-200-1-1-1-1-111111110000i3−i3i3−i3i3−i30i3−i300000000000000002-2-22000i3−i3i3−i3i3−i30i3−i30000-111-1000000
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χ33222-12222222-12-1-1-1-12-12-1-122-12-1222-1-1-1-12-1-1-1-2-2-1-1-1-1-122-1-1-1-1-10022000022-22211-2-2111111-2-211110000-100-1-10000-1-1-100-2-20000100100
χ34222-12222222-12-1-1-1-12-12-1-122-12-1222-1-1-1-12-1-1-1-2-2-1-1-1-1-122-1-1-1-1-100-2-20000-2-2-2-2-211-2-2111111-2-21111000010011000011100220000-100-100
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χ3722-222-1-2211-122-2-2-12-1-2-21111-1-1212-211-2-2-12-1-122-1-211-1-112-1-1112-20022-2-200-20022-1-1-1-1-1-1-2-211111100000-1100-1-1110002-20000000-11000
χ3822-222-1-2211-122-2-2-12-1-2-21111-1-1212-211-2-2-12-1-122-1-211-1-112-1-111-2200-2-22200-20022-1-1-1-1-1-1-2-2111111000001-10011-1-1000-2200000001-1000
χ3922-222-1-2211-122-2-2-12-1-2-21111-1-1212-211-2-2-12-1-1-2-2-1-211-1-112-1-1112-20022-2-200200-2-211111122-1-1-1-1-1-100000-1100-1-111000-2200000001-1000
χ4022-222-1-2211-122-2-2-12-1-2-21111-1-1212-211-2-2-12-1-1-2-2-1-211-1-112-1-111-2200-2-22200200-2-211111122-1-1-1-1-1-1000001-10011-1-10002-20000000-11000
χ4122-22-122-2-2-222-1222-1-1-21-2-2112-1-121-122-1-1-2-2-2-200-1111-11-1111-1-10000−i3i3i3−i3−i3i30i3−i3000000000000000022-2-2000−i3i3−i3i3i3−i30i3−i30000-1-111000000
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χ864-4044-2002i3−2i32-4-400-24-2002i3−2i32i3−2i322-400000000000−2222-202i3−2i3200000000000000000000−22222−22−22−200i6−i6i6−i6i6−i6000000000000000000000000000000
χ874-40-2440000-42-423−23-2-240000002-4200023−2323−23000022−22-200020000023−230000000000000−2222−22−22−226−6006−6−66000000000000000000000000000000
χ884-40-2440000-42-423−23-2-240000002-4200023−2323−230000−2222-200020000023−2300000000000002−2−22222−22−2−6600−666−6000000000000000000000000000000
χ894-40-2440000-42-4−2323-2-240000002-42000−2323−2323000022−22-2000200000−23230000000000000−2222−22−22−22−6600−666−6000000000000000000000000000000
χ904-40-2440000-42-4−2323-2-240000002-42000−2323−23230000−2222-2000200000−232300000000000002−2−22222−22−26−6006−6−66000000000000000000000000000000
χ914-40-24-200−2i32i322-423−231-2-200i3−i3−2i32i3-122000−3323−23003i−3i22−2210i3−i3-10003i−3i−330000000000000−22−22ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000
χ924-40-24-200−2i32i322-423−231-2-200i3−i3−2i32i3-122000−3323−23003i−3i−222210i3−i3-10003i−3i−3300000000000002−22−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
χ934-40-24-200−2i32i322-4−23231-2-200i3−i3−2i32i3-1220003−3−232300−3i3i22−2210i3−i3-1000−3i3i3−30000000000000−22−22−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000
χ944-40-24-200−2i32i322-4−23231-2-200i3−i3−2i32i3-1220003−3−232300−3i3i−222210i3−i3-1000−3i3i3−300000000000002−22−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ236−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
χ954-40-24-2002i3−2i322-423−231-2-200−i3i32i3−2i3-122000−3323−2300−3i3i22−2210−i3i3-1000−3i3i−330000000000000−22−22−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ236−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
χ964-40-24-2002i3−2i322-423−231-2-200−i3i32i3−2i3-122000−3323−2300−3i3i−222210−i3i3-1000−3i3i−3300000000000002−22−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000
χ974-40-24-2002i3−2i322-4−23231-2-200−i3i32i3−2i3-1220003−3−2323003i−3i22−2210−i3i3-10003i−3i3−30000000000000−22−22ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
χ984-40-24-2002i3−2i322-4−23231-2-200−i3i32i3−2i3-1220003−3−2323003i−3i−222210−i3i3-10003i−3i3−300000000000002−22−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000
χ99888-4-4-488-4-4-4-4-4-4-4222-4-42222222-4-4-42222-4-42200-12-1-1-1222-1-1-1-100000000000000000000000000000000000000000000000000000000000
χ100888-4-4-4-8-8-4-4-4-4-444222-4-42222222444-2-2-2-244-2-200-12-1-1-1-2-2-2111100000000000000000000000000000000000000000000000000000000000
χ10188-8-4-4-48-844-4-4-4-4-422244-2-2-2-2222-44-4222244-2-200-1-211-1-22-211-1-100000000000000000000000000000000000000000000000000000000000
χ10288-8-4-4-4-8844-4-4-44422244-2-2-2-22224-44-2-2-2-2-4-42200-1-211-12-22-1-11100000000000000000000000000000000000000000000000000000000000
χ1038-808-480000-8-84008-4-4000000-8440000000000000-40004000000000000000000000000000000000000000000000000000000000000000000
χ1048-808-4-400−4i34i34-8400-4-4200−4i34i32i3−2i34-240000000000000202i3−2i3-2000000000000000000000000000000000000000000000000000000000000000000
χ1058-808-4-4004i3−4i34-8400-4-42004i3−4i3−2i32i34-24000000000000020−2i32i3-2000000000000000000000000000000000000000000000000000000000000000000
χ1068-80-4-480000-84443−43-42-400000044-200043−43−23230000002000-200000−232300000000000000000000000000000000000000000000000000000000000
χ1078-80-4-480000-844−4343-42-400000044-2000−434323−230000002000-20000023−2300000000000000000000000000000000000000000000000000000000000
χ1088-80-4-4-400−4i34i344443−43222002i3−2i32i3−2i3-2-2-2000−2323−2323006i−6i00-10−i3i31000−3i3i3−300000000000000000000000000000000000000000000000000000000000
χ1098-80-4-4-400−4i34i3444−4343222002i3−2i32i3−2i3-2-2-200023−2323−2300−6i6i00-10−i3i310003i−3i−3300000000000000000000000000000000000000000000000000000000000
χ1108-80-4-4-4004i3−4i344443−4322200−2i32i3−2i32i3-2-2-2000−2323−232300−6i6i00-10i3−i310003i−3i3−300000000000000000000000000000000000000000000000000000000000
χ1118-80-4-4-4004i3−4i3444−434322200−2i32i3−2i32i3-2-2-200023−2323−23006i−6i00-10i3−i31000−3i3i−3300000000000000000000000000000000000000000000000000000000000

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