Finite Group Databasebeta

← Group #13170653

Character table — Group #13170653

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size1122222222244444444444466668888812121212121212121212121212121212121212242424363636363636367210811222222222444444444444666688888121212121212121212121212121212121212122424243636363636363672108
order12333466612123336661212121212122412123612121246666812121212122424242424242424121212226682424622266646661212666666121212121212241212661212124666681212121212242424242424242412121222668242462
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-111111-1-1-1-1-1-1-1-11111-111-1-1-1-1-11111111111111111111111111111111111111-111111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1
χ311111111111111111111111111111111-1111111-1-11111111111-1-1-1-1-1-1-1111-1-111111111111111111111111111111111-1111111-1-11111111111-1-1-1-1-1-1-1111-1-1
χ411111111111111111111111111111111-11111-11-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111111111111111111111111111111111-11111-11-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111
χ511111111111111111111111-1-1-1-1111111-1-1-1-11-111-1-111111111111-11-1-1-1-1-11-111111111111111111111111-1-1-1-1111111-1-1-1-11-111-1-111111111111-11-1-1-1-1-11-1
χ611111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-11
χ711111111111111111111111-1-1-1-111111-1-1-1-1-11-1-1-1-1-111111111-1-1-11-111-1-1-1-1111111111111111111111111-1-1-1-111111-1-1-1-1-11-1-1-1-1-111111111-1-1-11-111-1-1-1-11
χ811111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1
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χ1022222-2222-2-2222222-2-2-2-2-2-2-222222-2-2-20-2-2-2-20200220000000000000000000022222-2222-2-2222222-2-2-2-2-2-2-222222-2-2-20-2-2-2-202002200000000000000000000
χ112222-1222-1222-1-12-1-1-1-1-122222-1-1-1-1-1-1-122-1-1-102-1-1-1-1000000002-1-120-1-1000002222-1222-1222-1-12-1-1-1-1-122222-1-1-1-1-1-1-122-1-1-102-1-1-1-1000000002-1-120-1-100000
χ122222-1222-1222-1-12-1-1-1-1-122222-1-1-1-1-1-1-1-22-1-1-10211-1-100000000-211-2011000002222-1222-1222-1-12-1-1-1-1-122222-1-1-1-1-1-1-1-22-1-1-10211-1-100000000-211-201100000
χ132222-1222-1222-1-12-1-1-1-1-1222-2-211-1-1-1-1-12-21110-2-1-111000000002-1-1-2011000002222-1222-1222-1-12-1-1-1-1-1222-2-211-1-1-1-1-12-21110-2-1-111000000002-1-1-201100000
χ142222-1222-1222-1-12-1-1-1-1-1222-2-211-1-1-1-1-1-2-21110-2111100000000-21120-1-1000002222-1222-1222-1-12-1-1-1-1-1222-2-211-1-1-1-1-1-2-21110-2111100000000-21120-1-100000
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χ162222-1-222-1-2-22-1-12-1-1111-2-2-22-211-1-111102-1-1-10-2i3−i311000000000i3−i300i3−i3000002222-1-222-1-2-22-1-12-1-1111-2-2-22-211-1-111102-1-1-10-2i3−i311000000000i3−i300i3−i300000
χ172222-1-222-1-2-22-1-12-1-1111-2-2-2-22-1-1-1-11110-211102−i3i3-1-1000000000−i3i300i3−i3000002222-1-222-1-2-22-1-12-1-1111-2-2-2-22-1-1-1-11110-211102−i3i3-1-1000000000−i3i300i3−i300000
χ182222-1-222-1-2-22-1-12-1-1111-2-2-2-22-1-1-1-11110-211102i3−i3-1-1000000000i3−i300−i3i3000002222-1-222-1-2-22-1-12-1-1111-2-2-2-22-1-1-1-11110-211102i3−i3-1-1000000000i3−i300−i3i300000
χ19222-1222-1222-1-12-12-1222-1-1-10000-1-1-1-1-12000020220022-1-1-1-1-1-1-1-1-10200000-10222-1222-1222-1-12-12-1222-1-1-10000-1-1-1-1-12000020220022-1-1-1-1-1-1-1-1-10200000-10
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χ22222-1222-1222-1-12-12-1222-1-1-10000-1-1-1-1-1-20000-20-2-200-2-21111111110200000-10222-1222-1222-1-12-12-1222-1-1-10000-1-1-1-1-1-20000-20-2-200-2-21111111110200000-10
χ2322-1222-122-1-1-12-1-1-122-1-12-1-12222-1-12-1-10-12-1-12-100-1-1-1-122-1-1-1-100000002-1-10022-1222-122-1-1-12-1-1-122-1-12-1-12222-1-12-1-10-12-1-12-100-1-1-1-122-1-1-1-100000002-1-100
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χ2522-1222-122-1-1-12-1-1-122-1-12-1-1-2-2-2-2-1-12-1-101-211210011-1-122-1-1-1-10000000-2110022-1222-122-1-1-12-1-1-122-1-12-1-1-2-2-2-2-1-12-1-101-211210011-1-122-1-1-1-10000000-21100
χ2622-1222-122-1-1-12-1-1-122-1-12-1-1-2-2-2-2-1-12-1-101-211-21001111-2-2111100000002-1-10022-1222-122-1-1-12-1-1-122-1-12-1-1-2-2-2-2-1-12-1-101-211-21001111-2-2111100000002-1-100
χ2722-122-2-12211-12-1-1-12-211-2112-2-2-2-1-1-2110-12-1-10100113−30033−3−3000000003−30022-122-2-12211-12-1-1-12-211-2112-2-2-2-1-1-2110-12-1-10100113−30033−3−3000000003−300
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χ2922-122-2-12211-12-1-1-12-211-211-2222-1-1-21101-2110-100-1-13−30033−3−300000000−330022-122-2-12211-12-1-1-12-211-211-2222-1-1-21101-2110-100-1-13−30033−3−300000000−3300
χ3022-122-2-12211-12-1-1-12-211-211-2222-1-1-21101-2110-100-1-1−3300−3−333000000003−30022-122-2-12211-12-1-1-12-211-211-2222-1-1-21101-2110-100-1-1−3300−3−333000000003−300
χ31444-24-44-24-4-4-2-24-24-2-4-4-42220000-2-22220000000000000000000000000000000444-24-44-24-4-4-2-24-24-2-4-4-42220000-2-22220000000000000000000000000000000
χ32444-2-244-2-244-21-2-2-21-2-2-2-2-2-20000111114000000-2-20000000000-211000000000444-2-244-2-244-21-2-2-21-2-2-2-2-2-20000111114000000-2-20000000000-211000000000
χ33444-2-244-2-244-21-2-2-21-2-2-2-2-2-2000011111-40000002200000000002-1-1000000000444-2-244-2-244-21-2-2-21-2-2-2-2-2-2000011111-40000002200000000002-1-1000000000
χ34444-2-2-44-2-2-4-4-21-2-2-21222222000011-1-1-10000000−2i32i300000000000i3−i3000000000444-2-2-44-2-2-4-4-21-2-2-21222222000011-1-1-10000000−2i32i300000000000i3−i3000000000
χ35444-2-2-44-2-2-4-4-21-2-2-21222222000011-1-1-100000002i3−2i300000000000−i3i3000000000444-2-2-44-2-2-4-4-21-2-2-21222222000011-1-1-100000002i3−2i300000000000−i3i3000000000
χ3644-24-24-24-2-2-2-2-21-21-2-2114-2-244-2-211-2110-2-2110-200110000000000000000000044-24-24-24-2-2-2-2-21-21-2-2114-2-244-2-211-2110-2-2110-2001100000000000000000000
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χ3844-24-2-4-24-222-2-21-21-22-1-1-4224-422112-1-10-2-2110200-1-10000000000000000000044-24-2-4-24-222-2-21-21-22-1-1-4224-422112-1-10-2-2110200-1-100000000000000000000
χ3944-24-2-4-24-222-2-21-21-22-1-1-422-44-2-2112-1-1022-1-10-200110000000000000000000044-24-2-4-24-222-2-21-21-22-1-1-422-44-2-2112-1-1022-1-10-2001100000000000000000000
χ4044-2-244-2-24-2-21-2-21-2-24-2-2-211000011-21100000400000-2-2-2-2111100000000000044-2-244-2-24-2-21-2-21-2-24-2-2-211000011-21100000400000-2-2-2-21111000000000000
χ4144-2-244-2-24-2-21-2-21-2-24-2-2-211000011-21100000-4000002222-1-1-1-100000000000044-2-244-2-24-2-21-2-21-2-24-2-2-211000011-21100000-4000002222-1-1-1-1000000000000
χ4244-2-24-4-2-24221-2-21-2-2-4222-1-10000112-1-10000000000023−2300−3−33300000000000044-2-24-4-2-24221-2-21-2-2-4222-1-10000112-1-10000000000023−2300−3−333000000000000
χ4344-2-24-4-2-24221-2-21-2-2-4222-1-10000112-1-100000000000−23230033−3−300000000000044-2-24-4-2-24221-2-21-2-2-4222-1-10000112-1-100000000000−23230033−3−3000000000000
χ444-44440-4-4-400444-4-4-400000000004-400000000000000000000000000000000004-44440-4-4-400444-4-4-400000000004-40000000000000000000000000000000000
χ454-444-20-4-42004-2-2-4220000000023−23-2200000000000023−23000000000000000000004-444-20-4-42004-2-2-4220000000023−23-2200000000000023−2300000000000000000000
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χ494-4-24402-4-423−23-24-222-4023−23023−230000-22023−2300000000000000000000000000000004-4-24402-4-423−23-24-222-4023−23023−230000-22023−230000000000000000000000000000000
χ504-4-24402-4-4−2323-24-222-40−23230−23230000-220−232300000000000000000000000000000004-4-24402-4-4−2323-24-222-40−23230−23230000-220−23230000000000000000000000000000000
χ514-4-24-202-4223−23-2-212-120−33023−230023−231-10−330003-30000−33000000000000000000004-4-24-202-4223−23-2-212-120−33023−230023−231-10−330003-30000−3300000000000000000000
χ524-4-24-202-4223−23-2-212-120−33023−2300−23231-10−33000-3300003−3000000000000000000004-4-24-202-4223−23-2-212-120−33023−2300−23231-10−33000-3300003−300000000000000000000
χ534-4-24-202-42−2323-2-212-1203−30−23230023−231-103−3000-330000−33000000000000000000004-4-24-202-42−2323-2-212-1203−30−23230023−231-103−3000-330000−3300000000000000000000
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χ651111111111111111111111111111111111111-111111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111111111-1-1-1-11-1-111111
χ6611111111111111111111111111111111-1111111-1-11111111111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1-111
χ6711111111111111111111111111111111-11111-11-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-111-1-1111111111111-111111-1-1
χ6811111111111111111111111-1-1-1-1111111-1-1-1-11-111-1-111111111111-11-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11-1-111-1-1-1-1-1-1-1-1-1-1-11-111111-11
χ6911111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11111111111-1-1-11111-1-1-11-1
χ7011111111111111111111111-1-1-1-111111-1-1-1-1-11-1-1-1-1-111111111-1-1-11-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111-111111-1-1-1-1-1-1-1-1111-11-1-11111-1
χ7111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-11
χ7222222-2222-2-2222222-2-2-2-2-2-22-2-2-222-2-2-2022220-200-2-200000000000000000000-2-2-2-2-22-2-2-222-2-2-2-2-2-2222222-2222-2-22220-2-2-2-202002200000000000000000000
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χ1268-8-4-4-40444−4343222-2-2-2023−23023−230000-110−330000000000000000000000000000000-884440-4-4-443−43-2-2-22220−23230−232300001-103−30000000000000000000000000000000

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