Finite Group Databasebeta

← Group #13156598

Character table — Group #13156598

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size11112222222222222222224444444444444444444444446666666666666666666666668888888888121212121212121212121212121212121212121212121212181818181818181818181818242424242424242424727272727272216
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χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
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χ311111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ51111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-111-1
χ61111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-11
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1111111-1
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χ11222222-1222222-1-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
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χ13222222-1222222-1-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ14222222-1222222-1-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-10000000000000000
χ15222222-1-2-22222-1-1-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111000000003333−3−3−3−33333−3−3−3−3-1-1-1-1-2-2111100003333−3−3−3−300003333−3−3−3−322-2-2-1-1-1-111110000000000000000
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χ232222-12222-1-122222-122222-1-12-1-1-1-122-12-1-12-1-122-12-1-122222200002222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002-1-122-1-1-1-120-1-1000
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χ252222-12222-1-122222-122222-1-12-1-1-1-122-12-1-12-1-122-12-1-122-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-11111111111110000000000000000000000002-1-122-1-1-1-1-2011000
χ262222-12222-1-122222-122222-1-12-1-1-1-122-12-1-12-1-122-12-1-122-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000-211-2-2111120-1-1000
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χ3522-2-222-1002-22-21-11-2-2−3−3332-1-12-2-11-1111-200−33−3300−33−3322−2−222−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23-1-11100−3−33322−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ722−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23002-2−3−333-1-1110000000000000000
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χ3822-2-222-1002-22-21-11-2-2−3−3332-1-12-2-11-1111-200−33−3300−33−33−2−222−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23-1-11100−3−333−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23002-2−3−333-1-1110000000000000000
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χ402-22-222200-22-22-2-22-2-20000222-22-22-22-2-2-20000000000002−22−2−22−222−22−22−22−2−22−22−22−222-22-20000002−22−22−22−22−22−2−22−22−22−22−22−22-2200-22-2200000000000000000000
χ412-22-222200-22-22-2-22-2-20000222-22-22-22-2-2-2000000000000−22−222−22−2−22−22−22−222−22−22−22−22-22-2000000−22−22−22−22−22−222−22−22−22−22−22−2-2200-22-2200000000000000000000
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χ432-22-222-100-22-2211-1-2-23−33−32-1-1-221-11-111-2003−3−3300−333−32−22−22−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7-11-11003−33−32−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ72−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ72-200-11-113−33−30000000000000000
χ442-22-222-100-22-2211-1-2-23−33−32-1-1-221-11-111-2003−3−3300−333−32−22−2−22−22ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7-11-11003−33−32−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7-22001-11-1−33−330000000000000000
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χ1164-4-44-24-24-422-4-4-222-24-222-2-21-222-1-1221-2-2-2-4112224-1-1-2-200000000−232323−2323−23−2323000000001-1-11-221-1-1100003−3−33−333−30000000000000000000000000000000000000000
χ1174-4-44-24-2-4422-4-4-222-242-2-22-21-222-1-1221-2-224-1-1-2-2-2-411224-4-440000-222-2-222-2000000001-1-112-2-111-1-222-21-1-111-1-110000000000000000000000000000000000000000
χ1184-4-44-24-2-4422-4-4-222-242-2-22-21-222-1-1221-2-224-1-1-2-2-2-41122-444-400002-2-222-2-22000000001-1-112-2-111-12-2-22-111-1-111-10000000000000000000000000000000000000000
χ1194-4-44-2-244-422224-4-4-2-24-4-441-2-2-1-12222-2-21-22-2-2222-222-2-20000000000000000000000001-1-111-11-1-11000000000000000000000000000000000000000−2i32i3i3i3−i3−i30000000
χ1204-4-44-2-244-422224-4-4-2-24-4-441-2-2-1-12222-2-21-22-2-2222-222-2-20000000000000000000000001-1-111-11-1-110000000000000000000000000000000000000002i3−2i3−i3−i3i3i30000000
χ1214-4-44-2-24-4422224-4-4-2-2-444-41-2-2-1-12222-2-212-222-2-2-22-2-2220000000000000000000000001-1-11-11-111-10000000000000000000000000000000000000−2i32i300i3−i3i3−i30000000
χ1224-4-44-2-24-4422224-4-4-2-2-444-41-2-2-1-12222-2-212-222-2-2-22-2-2220000000000000000000000001-1-11-11-111-100000000000000000000000000000000000002i3−2i300−i3i3−i3i30000000
χ1238888-4-4-488-4-4-4-4-4-4-4-4-4-4-4-4-4222222222222-4-42222-4-42222000000000000000000000000-1-1-1-122-1-1-1-10000000000000000000000000000000000000000000000000000
χ1248888-4-4-4-8-8-4-4-4-4-4-4-4-4-4444422222222222244-2-2-2-244-2-2-2-2000000000000000000000000-1-1-1-1-2-211110000000000000000000000000000000000000000000000000000
χ12588-8-8-4-4800-44-44-88-84400002-4-42-2-44-4444-200000000000000000000000000000000000022-2-20000000000000000000000000000000000000000000000000000000000
χ12688-8-8-4-4-400-44-444-44444343−43−432222-22-22-2-2-2-200−2323−232300−2323−2323000000000000000000000000-1-1110033−3−30000000000000000000000000000000000000000000000000000
χ12788-8-8-4-4-400-44-444-4444−43−4343432222-22-22-2-2-2-20023−2323−230023−2323−23000000000000000000000000-1-11100−3−3330000000000000000000000000000000000000000000000000000
χ1288-88-8-4-48004-44-4-8-884400002-4-4-224-44-444-20000000000000000000000000000000000002-22-20000000000000000000000000000000000000000000000000000000000
χ1298-88-8-4-4-4004-44-444-44443−4343−43222-22-22-22-2-2-200−232323−230023−23−2323000000000000000000000000-11-11003−33−30000000000000000000000000000000000000000000000000000
χ1308-88-8-4-4-4004-44-444-444−4343−4343222-22-22-22-2-2-20023−23−232300−232323−23000000000000000000000000-11-1100−33−330000000000000000000000000000000000000000000000000000
χ1318-8-88-4-4-48-84444-444-4-4-444-4222-2-2-2-2-2-2222-4422-2-24-4-2-222000000000000000000000000-111-12-2-111-10000000000000000000000000000000000000000000000000000
χ1328-8-88-4-4-4-884444-444-4-44-4-44222-2-2-2-2-2-22224-4-2-222-4422-2-2000000000000000000000000-111-1-221-1-110000000000000000000000000000000000000000000000000000

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