Finite Group Databasebeta

← Group #13170576

Character table — Group #13170576

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size1122222222222224444444444444444444444466888888888888121212121212121212121212121212121212121212121212121212121218181818242424242424242424242424363636363636363672727272108108
order1223334466666121233366666666612121212121212121212128836666121212121212122224666666812122424242424242424242424242424242422446666666661212122444661212612121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-11111-1-11-1-11111111111111111-1-1-1-111-1-1-11111-1-1-1-111-1-1-1-1-1-1-111-1-1
χ31111111111111111111111111111111111111111111111111111-1-111-1-1-1-1111111111111111111111-1-1-1-1-1-1111-1-1-1-11111-1-11-1-1-1-111-1-1-1-1
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
χ611111111111111111111111111111111111111-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-11-1-11-1-1-1-111-1-111
χ711111111111111111111111111111111111111-1-1111111111111-1-111-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-111-1-1-1-1-1-1-11111
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
χ911-1111-11-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-111-1111-1-11-11-111-1-111-1-1-111111111-1-1-1-1-1-1-1-11-11-11-111111-1-1-1-1-1-11-111-11-1-111-11-1
χ1011-1111-11-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-111-1111-1-11-1-1111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-111111-1-1-11-111-11-1-11
χ1111-1111-11-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-111-1111-1-1-111-1-1-11111-1-1-111111111-1-1-1-1-1-1-1-1-11-11-11111-1-111-1-1-1-1-111-11-11-11-11-11
χ1211-1111-11-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-111-1111-1-1-11-11-1-111-1-1-11111111111-1-1-1-1-1-1-1-11-11-1-11-1-1-1-1-1111111-11-11-11-11-1-111-1
χ1311-1111-11-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11-1-1-111-1111-1-11-11-111-1-1111-1-1-1-1-1-1-1-1-1-1111111111-11-11-111111-1-1-1-1-11-11-11-11-11-1-11-11
χ1411-1111-11-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11-1-1-111-1111-1-11-1-1111-1-1-1-1111-1-1-1-1-1-1-1-111111111-11-111-1-1-1-111-1-1111-1-111-11-11-11-111-1
χ1511-1111-11-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11-1-1-111-1111-1-1-111-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-11-11-11111-1-111-1-1-111-1-1-11-111-11-11-1
χ1611-1111-11-1-1111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11-1-1-111-1111-1-1-11-11-1-111-1-1111-1-1-1-1-1-1-1-1111111111-11-1-11-1-1-1-1-111111-11-111-11-1-111-1-11
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χ2522222-1-2-2222-12-2-22-1-12-122-1-12-1-111-2-2-211-2-2-2-200-1-1-1-1-111111110000i3−i3i3−i3−i3i30−i3i30000000000000000-222-2000−i3i3i3−i3i3−i30−i3i300001-1-11000000
χ2622222-1-2-2222-12-2-22-1-12-122-1-12-1-111-2-2-211-2-2-2-200-1-1-1-1-111111110000i3−i3i3−i3i3−i30i3−i300000000000000002-2-22000i3−i3i3−i3i3−i30i3−i30000-111-1000000
χ272222-122222-122-1-1-1-12-12-1-122-12-1222-1-1-1-1-12-1-122-1-1-1-1-122-1-1-1-1-1002200002222222-1-1-1-1-1-122-1-1-1-1-1-1000000-1-1-10000-1-1-120020000-1-10000
χ282222-122222-122-1-1-1-12-12-1-122-12-1222-1-1-1-1-12-1-122-1-1-1-1-122-1-1-1-1-100-2-20000-2-22-2-222-1-1-1-1-1-122-1-1-1-1-1-10000001110000111-200-20000110000
χ292222-122222-122-1-1-1-12-12-1-122-12-1222-1-1-1-1-12-1-1-2-2-1-1-1-1-122-1-1-1-1-10022000022-222-2-2111111-2-2111111000000-1-1-10000-1-1-1-200-20000110000
χ302222-122222-122-1-1-1-12-12-1-122-12-1222-1-1-1-1-12-1-1-2-2-1-1-1-1-122-1-1-1-1-100-2-20000-2-2-2-2-2-2-2111111-2-2111111000000111000011120020000-1-10000
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χ32222-12222-1-122-122-12-122-1-1-1-1-1-1222-1-1-1222-1-1-122-12-1-1-1-1-12-1-1-1-1-2-200-2-2-2-200200-1-122-1-1-1-1-1-122-1-1-1-100001100011110000-2-200000001100
χ33222-12222-1-122-122-12-122-1-1-1-1-1-1222-1-1-1222-1-1-1-2-2-12-1-1-1-1-12-1-1-1-12200222200-20011-2-2111111-2-211110000-1-1000-1-1-1-10000-2-200000001100
χ34222-12222-1-122-122-12-122-1-1-1-1-1-1222-1-1-1222-1-1-1-2-2-12-1-1-1-1-12-1-1-1-1-2-200-2-2-2-200-20011-2-2111111-2-2111100001100011110000220000000-1-100
χ3522-22222-2-2-222222222-2-2-2-2-2-2222-2222222-2-2-2-2002-2-2-22-22-2-2-2220000000000000000000000000000022-2-2000000000000000022-2-2000000
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χ3722-222-12-2-2-22-12222-1-1-21-2-2112-1-11-1222-1-1-2-2-2-200-1111-11-1111-1-10000−i3i3i3−i3−i3i30i3−i3000000000000000022-2-2000−i3i3−i3i3i3−i30i3−i30000-1-111000000
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χ3922-222-12-2-2-22-12222-1-1-21-2-2112-1-11-1222-1-1-2-2-2-200-1111-11-1111-1-10000i3−i3−i3i3−i3i30i3−i30000000000000000-2-222000−i3i3i3−i3−i3i30i3−i3000011-1-1000000
χ4022-222-12-2-2-22-12222-1-1-21-2-2112-1-11-1222-1-1-2-2-2-200-1111-11-1111-1-10000i3−i3−i3i3i3−i30−i3i3000000000000000022-2-2000i3−i3i3−i3−i3i30−i3i30000-1-111000000
χ4122-222-1-22-2-22-12-2-22-1-1-21-2-2112-1-1-11-2-2-211222200-1111-1-11-1-1-1112-22-2-1-111-1-101100000000000000002-22-22-22-1-1-1-111-2110000-11-11000000
χ4222-222-1-22-2-22-12-2-22-1-1-21-2-2112-1-1-11-2-2-211222200-1111-1-11-1-1-1112-2-22-1-111110-1-10000000000000000-22-222-2-211-1-1112-1-100001-11-1000000
χ4322-222-1-22-2-22-12-2-22-1-1-21-2-2112-1-1-11-2-2-211222200-1111-1-11-1-1-111-222-211-1-1-1-10110000000000000000-22-22-222-1-111-1-1-21100001-11-1000000
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χ4522-22-12-22-2-2-12211-1-121-211-2-2-12-12-2-21111-12-1-122-1111-12-2-1-1-111002-2000022-2-2-222-1-1-1-1-1-1-2-2111111000000-1-1-10000111-200200001-10000
χ4622-22-12-22-2-2-12211-1-121-211-2-2-12-12-2-21111-12-1-122-1111-12-2-1-1-11100-220000-2-2-22222-1-1-1-1-1-1-2-21111110000001110000-1-1-1200-20000-110000
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χ924-40-2-2400−2i32i32-4223−231-2-200i3−i3−2i32i3-122000−3323−23003i−3i2i2−2i210i3−i3-10003i−3i−330000000000000−i2i2−i2i2−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
χ934-40-2-2400−2i32i32-42−23231-2-200i3−i3−2i32i3-1220003−3−232300−3i3i−2i22i210i3−i3-1000−3i3i3−30000000000000i2−i2i2−i2−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ236−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
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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
χ10188-8-4-4-48-844-4-4-4-4-422244-2-2-2-22224-4-4222244-2-200-1-211-1-22-211-1-100000000000000000000000000000000000000000000000000000000000
χ10288-8-4-4-4-8844-4-4-44422244-2-2-2-2222-444-2-2-2-2-4-42200-1-211-12-22-1-11100000000000000000000000000000000000000000000000000000000000
χ1038-8088-40000-84-8008-4-4000000-8440000000000000-40004000000000000000000000000000000000000000000000000000000000000000000
χ1048-808-4-4000044-843−43-42-400000044-200043−43−23230000002000-200000−232300000000000000000000000000000000000000000000000000000000000
χ1058-808-4-4000044-8−4343-42-400000044-2000−434323−230000002000-20000023−2300000000000000000000000000000000000000000000000000000000000
χ1068-80-48-400−4i34i3-84400-4-4200−4i34i32i3−2i34-240000000000000202i3−2i3-2000000000000000000000000000000000000000000000000000000000000000000
χ1078-80-48-4004i3−4i3-84400-4-42004i3−4i3−2i32i34-24000000000000020−2i32i3-2000000000000000000000000000000000000000000000000000000000000000000
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.