Finite Group Databasebeta

← Group #13181131

Character table — Group #13181131

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122224444444488888888181818181818181818181818181818181818363636363636363636363636111122224444444488888888181818181818181818181818181818181818363636363636363636363636
order124436121233661212121233661212121224668888121224242424242424242244666612121212224466121266661212121266661212121224668888121224242424242424242244666612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-11-111-1-111-1-11111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ41111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-11-1-111-1-1111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ511-1-111-1-11111-1-1-1-11111-1-1-1-1-11-1-111-1-1111111-1-1-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-1-111-1-1111111-1-1-1-111-1-11111-1-1-1-1
χ611-1-111-1-11111-1-1-1-11111-1-1-1-1-11-1-111-1-1111111-1-1-1-1-1-111-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-1-111-1-1111111-1-1-1-1-1-111-1-1-1-11111
χ711-1-111-1-11111-1-1-1-11111-1-1-1-1-11-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-1-1-1-11111-1-1-1-111111-1-1111-1-1-1-111
χ811-1-111-1-11111-1-1-1-11111-1-1-1-1-11-1-1-1-11111-1-1-1-11111-111-1-1-11111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-1-1-1-11111-1-1-1-11111-111-1-1-11111-1-1
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χ1622-2-2-1-1112222-2-2-2-2-1-1-1-111112-2-1-1000011−3−33333−3−300000000000022-2-2-1-1112222-2-2-2-2-1-1-1-111112-2-1-1000011−3−33333−3−3000000000000
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χ252-2−2i2i2-2−2i2i22-2-2−2i−2i2i2i22-2-2−2i−2i2i2i00002−2i2−i2002−22−2i2−i2i2−i20000000000002-2−2i2i2-2−2i2i22-2-2−2i−2i2i2i22-2-2−2i−2i2i2i00002−2i2−i2002−22−2i2−i2i2−i2000000000000
χ262-2−2i2i2-2−2i2i22-2-2−2i−2i2i2i22-2-2−2i−2i2i2i0000−22−i2i200−22−22−i2i2−i2i20000000000002-2−2i2i2-2−2i2i22-2-2−2i−2i2i2i22-2-2−2i−2i2i2i0000−22−i2i200−22−22−i2i2−i2i2000000000000
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χ31444444441-21-21-21-21-21-21-21-2000000000000000000020200-1-100-1-1444444441-21-21-21-21-21-21-21-2000000000000000000020200-1-100-1-1
χ32444444441-21-21-21-21-21-21-21-20000000000000000000-20-200110011444444441-21-21-21-21-21-21-21-20000000000000000000-20-200110011
χ3344444444-21-21-21-21-21-21-21-210000000000000000002020-1-100-1-10044444444-21-21-21-21-21-21-21-210000000000000000002020-1-100-1-100
χ3444444444-21-21-21-21-21-21-21-21000000000000000000-20-201100110044444444-21-21-21-21-21-21-21-21000000000000000000-20-2011001100
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χ3744-4-444-4-4-21-212-12-1-21-212-12-100000000000000000020-20-1-100110044-4-444-4-4-21-212-12-1-21-212-12-100000000000000000020-20-1-1001100
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χ454-4−4i4i4-4−4i4i-212-12i−i−2ii-212-12i−i−2ii0000000000000000000000−i3i300−33004-4−4i4i4-4−4i4i-212-12i−i−2ii-212-12i−i−2ii0000000000000000000000−i3i300−3300
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χ478888-4-4-4-42-42-42-42-4-12-12-12-120000000000000000000000000000008888-4-4-4-42-42-42-42-4-12-12-12-12000000000000000000000000000000
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χ672222-1-1-1-122222222-1-1-1-1-1-1-1-1-2-211000011−3−333−3−333000000000000-2-2-2-21111-2-2-2-2-2-2-2-21111111122-1-10000-1-133−3−333−3−3000000000000
χ6822-2-222-2-22222-2-2-2-22222-2-2-2-22-2220000-2-200000000000000000000-2-222-2-222-2-2-2-22222-2-2-2-22222-22-2-200002200000000000000000000
χ6922-2-2-1-1112222-2-2-2-2-1-1-1-111112-2-1-100001133−3−3−3−333000000000000-2-22211-1-1-2-2-2-222221111-1-1-1-1-22110000-1-1−3−33333−3−3000000000000
χ7022-2-2-1-1112222-2-2-2-2-1-1-1-111112-2-1-1000011−3−33333−3−3000000000000-2-22211-1-1-2-2-2-222221111-1-1-1-1-22110000-1-133−3−3−3−333000000000000
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χ732-22i−2i2-22i−2i22-2-22i2i−2i−2i22-2-22i2i−2i−2i00002−2−i2i2002−22−2−i2i2−i2i2000000000000-22−2i2i-22−2i2i-2-222−2i−2i2i2i-2-222−2i−2i2i2i0000−22i2−i200−22−22i2−i2i2−i2000000000000
χ742-22i−2i2-22i−2i22-2-22i2i−2i−2i22-2-22i2i−2i−2i0000−22i2−i200−22−22i2−i2i2−i2000000000000-22−2i2i-22−2i2i-2-222−2i−2i2i2i-2-222−2i−2i2i2i00002−2−i2i2002−22−2−i2i2−i2i2000000000000
χ752-22i−2i-11−ii22-2-22i2i−2i−2i-1-111−i−iii00−i3i32−2−i2i23−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000-22−2i2i1-1i−i-2-222−2i−2i2i2i11-1-1ii−i−i00i3−i3−22i2−i2−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ762-22i−2i-11−ii22-2-22i2i−2i−2i-1-111−i−iii00−i3i3−22i2−i23−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000-22−2i2i1-1i−i-2-222−2i−2i2i2i11-1-1ii−i−i00i3−i32−2−i2i2−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ772-22i−2i-11−ii22-2-22i2i−2i−2i-1-111−i−iii00i3−i32−2−i2i2−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000-22−2i2i1-1i−i-2-222−2i−2i2i2i11-1-1ii−i−i00−i3i3−22i2−i23−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ782-22i−2i-11−ii22-2-22i2i−2i−2i-1-111−i−iii00i3−i3−22i2−i2−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000-22−2i2i1-1i−i-2-222−2i−2i2i2i11-1-1ii−i−i00−i3i32−2−i2i23−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ792-2−2i2i2-2−2i2i22-2-2−2i−2i2i2i22-2-2−2i−2i2i2i00002−2i2−i2002−22−2i2−i2i2−i2000000000000-222i−2i-222i−2i-2-2222i2i−2i−2i-2-2222i2i−2i−2i0000−22−i2i200−22−22−i2i2−i2i2000000000000
χ802-2−2i2i2-2−2i2i22-2-2−2i−2i2i2i22-2-2−2i−2i2i2i0000−22−i2i200−22−22−i2i2−i2i2000000000000-222i−2i-222i−2i-2-2222i2i−2i−2i-2-2222i2i−2i−2i00002−2i2−i2002−22−2i2−i2i2−i2000000000000
χ812-2−2i2i-11i−i22-2-2−2i−2i2i2i-1-111ii−i−i00−i3i32−2i2−i2−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000-222i−2i1-1−ii-2-2222i2i−2i−2i11-1-1−i−iii00i3−i3−22−i2i23−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ822-2−2i2i-11i−i22-2-2−2i−2i2i2i-1-111ii−i−i00−i3i3−22−i2i2−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000-222i−2i1-1−ii-2-2222i2i−2i−2i11-1-1−i−iii00i3−i32−2i2−i23−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ832-2−2i2i-11i−i22-2-2−2i−2i2i2i-1-111ii−i−i00i3−i32−2i2−i23−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000-222i−2i1-1−ii-2-2222i2i−2i−2i11-1-1−i−iii00−i3i3−22−i2i2−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ842-2−2i2i-11i−i22-2-2−2i−2i2i2i-1-111ii−i−i00i3−i3−22−i2i23−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000-222i−2i1-1−ii-2-2222i2i−2i−2i11-1-1−i−iii00−i3i32−2i2−i2−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ85444444441-21-21-21-21-21-21-21-2000000000000000000020200-1-100-1-1-4-4-4-4-4-4-4-4-12-12-12-12-12-12-12-120000000000000000000-20-200110011
χ86444444441-21-21-21-21-21-21-21-20000000000000000000-20-200110011-4-4-4-4-4-4-4-4-12-12-12-12-12-12-12-12000000000000000000020200-1-100-1-1
χ8744444444-21-21-21-21-21-21-21-210000000000000000002020-1-100-1-100-4-4-4-4-4-4-4-42-12-12-12-12-12-12-12-1000000000000000000-20-2011001100
χ8844444444-21-21-21-21-21-21-21-21000000000000000000-20-2011001100-4-4-4-4-4-4-4-42-12-12-12-12-12-12-12-10000000000000000002020-1-100-1-100
χ8944-4-444-4-41-21-2-12-121-21-2-12-12000000000000000000020-200-1-10011-4-444-4-444-12-121-21-2-12-121-21-20000000000000000000-202001100-1-1
χ9044-4-444-4-41-21-2-12-121-21-2-12-120000000000000000000-202001100-1-1-4-444-4-444-12-121-21-2-12-121-21-2000000000000000000020-200-1-10011
χ9144-4-444-4-4-21-212-12-1-21-212-12-100000000000000000020-20-1-1001100-4-444-4-4442-12-1-21-212-12-1-21-21000000000000000000-20201100-1-100
χ9244-4-444-4-4-21-212-12-1-21-212-12-1000000000000000000-20201100-1-100-4-444-4-4442-12-1-21-212-12-1-21-2100000000000000000020-20-1-1001100
χ934-44i−4i4-44i−4i1-2-12i−2i−i2i1-2-12i−2i−i2i000000000000000000000000−i3i3003−3-44−4i4i-44−4i4i-121-2−i2ii−2i-121-2−i2ii−2i000000000000000000000000i3−i300−33
χ944-44i−4i4-44i−4i1-2-12i−2i−i2i1-2-12i−2i−i2i000000000000000000000000i3−i300−33-44−4i4i-44−4i4i-121-2−i2ii−2i-121-2−i2ii−2i000000000000000000000000−i3i3003−3
χ954-44i−4i4-44i−4i-212-1−2ii2i−i-212-1−2ii2i−i0000000000000000000000−i3i3003−300-44−4i4i-44−4i4i2-1-212i−i−2ii2-1-212i−i−2ii0000000000000000000000i3−i300−3300
χ964-44i−4i4-44i−4i-212-1−2ii2i−i-212-1−2ii2i−i0000000000000000000000i3−i300−3300-44−4i4i-44−4i4i2-1-212i−i−2ii2-1-212i−i−2ii0000000000000000000000−i3i3003−300
χ974-4−4i4i4-4−4i4i1-2-12−i2ii−2i1-2-12−i2ii−2i000000000000000000000000−i3i300−33-444i−4i-444i−4i-121-2i−2i−i2i-121-2i−2i−i2i000000000000000000000000i3−i3003−3
χ984-4−4i4i4-4−4i4i1-2-12−i2ii−2i1-2-12−i2ii−2i000000000000000000000000i3−i3003−3-444i−4i-444i−4i-121-2i−2i−i2i-121-2i−2i−i2i000000000000000000000000−i3i300−33
χ994-4−4i4i4-4−4i4i-212-12i−i−2ii-212-12i−i−2ii0000000000000000000000−i3i300−3300-444i−4i-444i−4i2-1-21−2ii2i−i2-1-21−2ii2i−i0000000000000000000000i3−i3003−300
χ1004-4−4i4i4-4−4i4i-212-12i−i−2ii-212-12i−i−2ii0000000000000000000000i3−i3003−300-444i−4i-444i−4i2-1-21−2ii2i−i2-1-21−2ii2i−i0000000000000000000000−i3i300−3300
χ1018888-4-4-4-42-42-42-42-4-12-12-12-12000000000000000000000000000000-8-8-8-84444-24-24-24-241-21-21-21-2000000000000000000000000000000
χ1028888-4-4-4-4-42-42-42-422-12-12-12-1000000000000000000000000000000-8-8-8-844444-24-24-24-2-21-21-21-21000000000000000000000000000000
χ10388-8-8-4-4442-42-4-24-24-12-121-21-2000000000000000000000000000000-8-88844-4-4-24-242-42-41-21-2-12-12000000000000000000000000000000
χ10488-8-8-4-444-42-424-24-22-12-1-21-21000000000000000000000000000000-8-88844-4-44-24-2-42-42-21-212-12-1000000000000000000000000000000
χ1058-88i−8i-44−4i4i2-4-242i−4i−2i4i-121-2−i2ii−2i000000000000000000000000000000-88−8i8i4-44i−4i-242-4−2i4i2i−4i1-2-12i−2i−i2i000000000000000000000000000000
χ1068-88i−8i-44−4i4i-424-2−4i2i4i−2i2-1-212i−i−2ii000000000000000000000000000000-88−8i8i4-44i−4i4-2-424i−2i−4i2i-212-1−2ii2i−i000000000000000000000000000000
χ1078-8−8i8i-444i−4i2-4-24−2i4i2i−4i-121-2i−2i−i2i000000000000000000000000000000-888i−8i4-4−4i4i-242-42i−4i−2i4i1-2-12−i2ii−2i000000000000000000000000000000
χ1088-8−8i8i-444i−4i-424-24i−2i−4i2i2-1-21−2ii2i−i000000000000000000000000000000-888i−8i4-4−4i4i4-2-42−4i2i4i−2i-212-12i−i−2ii000000000000000000000000000000

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