Finite Group Databasebeta

← Group #13170641

Character table — Group #13170641

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size112222222222222444444444444444444444446666668888888888881212121212121212121212121212121212121212121212181818182424242424242424242424242424363636363636363672727272108108
order1223334466666121233366666666612121212121212121212128824242424366661212121212121244888242424242424242424242424242424242424224412121212121212122424242424242444661212612121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1
χ311111111111111111111111111111111111111111111111111111111-1-11111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-11-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-111
χ511111111111111111111111111111111111111-1-1-1-1-1-111111111111111-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-11-1-1-1-111-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911-1111-11-1-111111111-1-1-1-1-1-1111-1-1-1-1-11111111111111-1-1-11-11-111-1-11-1-11-1-1-111-1-1111111-1-1-1-1-1-11-11-11-11-111-1-1111-1-1-111-1-11-11-11-11-11-1
χ1011-1111-11-1-111111111-1-1-1-1-1-1111-1-1-1-1-11111111111111-1-1-11-11-111-1-11-1-1-11-1-1-1-111111111-1-1-1-1-1-1-11-111-11-111-1-1-1-1-1111-11-11-11-11-111-1-11
χ1111-1111-11-1-111111111-1-1-1-1-1-1111-1-1-1-1-11111111111111-1-1-11-11-111-1-1-11-11-1-1-111-1-1111111-1-1-1-1-1-11-11-1-11-11-1-111111-1-1-1-1-1111-11-1-11-11-11
χ1211-1111-11-1-111111111-1-1-1-1-1-1111-1-1-1-1-11111111111111-1-1-11-11-111-1-1-11-1-11-1-1-1-111111111-1-1-1-1-1-1-11-11-11-11-1-111-1-1-11111-11-1-11-111-1-111-1
χ1311-1111-11-1-111111111-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1-11-1-1-11-11-111-1-11-111-11111-1-1-1-1-1-1-1-1111111-11-111-11-111-1-1111-1-1-11-11-1-11-111-1-11-11
χ1411-1111-11-1-111111111-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1-11-1-1-11-11-111-1-11-11-1111-1-111-1-1-1-1-1-11111111-11-11-11-111-1-1-1-1-1111-1-1111-11-1-11-111-1
χ1511-1111-11-1-111111111-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1-11-1-1-11-11-111-1-1-1111-11111-1-1-1-1-1-1-1-1111111-11-11-11-11-1-111111-1-1-1-11-11-11-11-111-11-1
χ1611-1111-11-1-111111111-1-1-1-1-1-1111-1-1-1-1-1111111-1-1-1-1-1-11-1-1-11-11-111-1-1-111-1111-1-111-1-1-1-1-1-11111111-11-1-11-11-1-111-1-1-111111-1-11-11-11-11-1-11
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χ1922222-122222-12222-1-12-122-1-12-1-12-1222-1222-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1220220022220000000000000000-1-122-1-1-1-1-1-1-1-1-1-120020000-1-10000
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χ242222-122222-122-1-1-12-1-12-1-122-1-12-122-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1002-2-2-1-1111122-1-1-1-122-1-1-1-1-2-2-2-200000000-211-21100001111000000
χ252222-122222-122-1-1-12-1-12-1-122-1-12-122-1-122-1-1-1-1-2-21111-1-1-1-1-1-122-1-1-1-100-22211-1-1-1-1-2-21111-2-21111-2-2-2-2000000002-1-12-1-100001111000000
χ262222-122222-122-1-1-12-1-12-1-122-1-12-122-1-122-1-1-1-1-2-21111-1-1-1-1-1-122-1-1-1-100-2-2-2111111-2-21111-2-21111222200000000-211-2110000-1-1-1-1000000
χ272222-12-2-222-12211-12-1-12-1-122-1-121-2-211-2-211110033−3−3-1-1-1-1-11-2-21111000003−33−33−30033−3−30033−3−32-2-220000000003−303−30000-111-1000000
χ282222-12-2-222-12211-12-1-12-1-122-1-121-2-211-2-211110033−3−3-1-1-1-1-11-2-21111000003−3−33−330033−3−30033−3−3-222-2000000000−330−3300001-1-11000000
χ292222-12-2-222-12211-12-1-12-1-122-1-121-2-211-2-2111100−3−333-1-1-1-1-11-2-2111100000−333−33−300−3−33300−3−333-222-20000000003−303−300001-1-11000000
χ302222-12-2-222-12211-12-1-12-1-122-1-121-2-211-2-2111100−3−333-1-1-1-1-11-2-2111100000−33−33−3300−3−33300−3−3332-2-22000000000−330−330000-111-1000000
χ31222-12222-1-122-122-1-1222-1-1-1-1-12-122-1-1-12-1-1-122222222-12-1-1-12-1-1-1-1-1-122200220000-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-10000000220000000-1-100
χ32222-12222-1-122-122-1-1222-1-1-1-1-12-122-1-1-12-1-1-122222222-12-1-1-12-1-1-1-1-1-1-2-2200220000-1-1-1-1-1-1-1-1-1-1-1-10000-2-21111110000000-2-200000001100
χ33222-12222-1-122-122-1-1222-1-1-1-1-12-122-1-1-12-1-1-122-2-2-2-2-2-2-12-1-1-12-1-1-1-1-1-122-200-2-20000111111111111000022-1-1-1-1-1-10000000-2-200000001100
χ34222-12222-1-122-122-1-1222-1-1-1-1-12-122-1-1-12-1-1-122-2-2-2-2-2-2-12-1-1-12-1-1-1-1-1-1-2-2-200-2-200001111111111110000-2-21111110000000220000000-1-100
χ3522-22222-2-2-2222-2-2222-2-2-2-2-2-222222222-2-2-2-2-2-20000002-2-2-222-22-2-2220000000000000000000000022-2-200000000000000000022-2-2000000
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χ3722-222-1-22-2-22-12222-1-1-21-2-2112-1-1-21-2-2-2-1222-1-1000000-1111-11-11-1-1112-202-20022-2-20000000000000000-112-2-1-111-1-1-1111200-20000-110000
χ3822-222-1-22-2-22-12222-1-1-21-2-2112-1-1-21-2-2-2-1222-1-1000000-1111-11-11-1-1112-20-2200-2-2220000000000000000-112-2-1-111111-1-1-1-200200001-10000
χ3922-222-1-22-2-22-12222-1-1-21-2-2112-1-1-21-2-2-2-1222-1-1000000-1111-11-11-1-111-2202-20022-2-200000000000000001-1-2211-1-1-1-1-1111-200200001-10000
χ4022-222-1-22-2-22-12222-1-1-21-2-2112-1-1-21-2-2-2-1222-1-1000000-1111-11-11-1-111-220-2200-2-22200000000000000001-1-2211-1-1111-1-1-1200-20000-110000
χ4122-22-122-2-2-2-12211-12-11-211-2-2-1-12-122-1-1-2-211110033−3−3-1111-1-1-2211-1-100000−333−3−330033−3−300−3−33322-2-20000000003−30−330000-1-111000000
χ4222-22-122-2-2-2-12211-12-11-211-2-2-1-12-122-1-1-2-211110033−3−3-1111-1-1-2211-1-100000−33−333−30033−3−300−3−333-2-222000000000−3303−3000011-1-1000000
χ4322-22-122-2-2-2-12211-12-11-211-2-2-1-12-122-1-1-2-2111100−3−333-1111-1-1-2211-1-1000003−33−3−3300−3−3330033−3−3-2-2220000000003−30−33000011-1-1000000
χ4422-22-122-2-2-2-12211-12-11-211-2-2-1-12-122-1-1-2-2111100−3−333-1111-1-1-2211-1-1000003−3−333−300−3−3330033−3−322-2-2000000000−3303−30000-1-111000000
χ4522-22-12-22-2-2-122-1-1-12-11-211-2-2-1-121-2-21122-1-1-1-122-1-1-1-1-1111-112-2-1-11100-22-211-1-11122-1-1-1-1-2-211112-22-2000000002-1-1-2110000-11-11000000
χ4622-22-12-22-2-2-122-1-1-12-11-211-2-2-1-121-2-21122-1-1-1-122-1-1-1-1-1111-112-2-1-11100-2-221111-1-122-1-1-1-1-2-21111-22-2200000000-2112-1-100001-11-1000000
χ4722-22-12-22-2-2-122-1-1-12-11-211-2-2-1-121-2-21122-1-1-1-1-2-21111-1111-112-2-1-1110022-2-1-1-1-111-2-2111122-1-1-1-1-22-22000000002-1-1-21100001-11-1000000
χ4822-22-12-22-2-2-122-1-1-12-11-211-2-2-1-121-2-21122-1-1-1-1-2-21111-1111-112-2-1-111002-22-1-111-1-1-2-2111122-1-1-1-12-22-200000000-2112-1-10000-11-11000000
χ4922-2-122-221122-122-1-12-2-21111-12-1-2-21112-1-1-122222222-1-211-1-2-11-1-1112-2-200-2-20000-1-1-1-1-1-111111100002-2-11-1-11100000002-20000000-1100
χ5022-2-122-221122-122-1-12-2-21111-12-1-2-21112-1-1-122222222-1-211-1-2-11-1-111-22-200-2-20000-1-1-1-1-1-11111110000-221-111-1-10000000-2200000001-100
χ5122-2-122-221122-122-1-12-2-21111-12-1-2-21112-1-1-122-2-2-2-2-2-2-1-211-1-2-11-1-1112-2200220000111111-1-1-1-1-1-100002-2-11-1-1110000000-2200000001-100
χ5222-2-122-221122-122-1-12-2-21111-12-1-2-21112-1-1-122-2-2-2-2-2-2-1-211-1-2-11-1-111-22200220000111111-1-1-1-1-1-10000-221-111-1-100000002-20000000-1100
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χ914-40-2-2400−2i32i32-4223−231-2-200i3−i3−2i32i3-1220003i−3i00−3323−2322−222ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2310i3−i3-1000−333i−3i00000000000−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ2300000000000000000000000000000000
χ924-40-2-2400−2i32i32-4223−231-2-200i3−i3−2i32i3-1220003i−3i00−3323−23−2222−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2310i3−i3-1000−333i−3i000000000002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−i6i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ2300000000000000000000000000000000
χ934-40-2-2400−2i32i32-42−23231-2-200i3−i3−2i32i3-122000−3i3i003−3−232322−222ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ710i3−i3-10003−3−3i3i00000000000−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7i6−i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ2300000000000000000000000000000000
χ944-40-2-2400−2i32i32-42−23231-2-200i3−i3−2i32i3-122000−3i3i003−3−2323−2222−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ710i3−i3-10003−3−3i3i000000000002−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−i6i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ2300000000000000000000000000000000
χ954-40-2-24002i3−2i32-4223−231-2-200−i3i32i3−2i3-122000−3i3i00−3323−2322−222ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2310−i3i3-1000−33−3i3i00000000000−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−i6i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ2300000000000000000000000000000000
χ964-40-2-24002i3−2i32-4223−231-2-200−i3i32i3−2i3-122000−3i3i00−3323−23−2222−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2310−i3i3-1000−33−3i3i000000000002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ2300000000000000000000000000000000
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χ984-40-2-24002i3−2i32-42−23231-2-200−i3i32i3−2i3-1220003i−3i003−3−2323−2222−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ710−i3i3-10003−33i−3i000000000002−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7i6−i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ2300000000000000000000000000000000
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χ100888-4-4-4-8-8-4-4-4-4-444222-4-42222222444-2-244-2-2-2-2000000-12-1-1-1-2-2-211110000000000000000000000000000000000000000000000000000000
χ10188-8-4-4-48-844-4-4-44422244-2-2-2-2222-4-4-42244-2-2-2-2000000-1-211-12-2211-1-10000000000000000000000000000000000000000000000000000000
χ10288-8-4-4-4-8844-4-4-4-4-422244-2-2-2-2222444-2-2-4-42222000000-1-211-1-22-2-1-1110000000000000000000000000000000000000000000000000000000
χ1038-8088-40000-84-8008-4-4000000-84400000000000000000-4000400000000000000000000000000000000000000000000000000000000000000
χ1048-808-4-4000044-843−43-4-420000004-24000000043−43−23230000002000-2000−2323000000000000000000000000000000000000000000000000000000000
χ1058-808-4-4000044-8−4343-4-420000004-240000000−434323−230000002000-200023−23000000000000000000000000000000000000000000000000000000000
χ1068-80-48-400−4i34i3-84400-42-400−4i34i32i3−2i344-200000000000000000202i3−2i3-200000000000000000000000000000000000000000000000000000000000000
χ1078-80-48-4004i3−4i3-84400-42-4004i3−4i3−2i32i344-20000000000000000020−2i32i3-200000000000000000000000000000000000000000000000000000000000000
χ1088-80-4-4-400−4i34i344443−43222002i3−2i32i3−2i3-2-2-20006i−6i00−2323−2323000000-10−i3i310003−3−3i3i0000000000000000000000000000000000000000000000000000000
χ1098-80-4-4-400−4i34i3444−4343222002i3−2i32i3−2i3-2-2-2000−6i6i0023−2323−23000000-10−i3i31000−333i−3i0000000000000000000000000000000000000000000000000000000
χ1108-80-4-4-4004i3−4i344443−4322200−2i32i3−2i32i3-2-2-2000−6i6i00−2323−2323000000-10i3−i310003−33i−3i0000000000000000000000000000000000000000000000000000000
χ1118-80-4-4-4004i3−4i3444−434322200−2i32i3−2i32i3-2-2-20006i−6i0023−2323−23000000-10i3−i31000−33−3i3i0000000000000000000000000000000000000000000000000000000

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