Finite Group Databasebeta

← Group #13155506

Character table — Group #13155506

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222222244444444444444444444444488888888881212121212121212121212121212121212121212121212121212121212121212121212121212181818182424242424242424363636363636363672727272108108
order12442333466666121212121212121233366666666612121212121212121212121236666121212121288888824242424242424242424242424242424242424242424242424242424242424242244242424242424242466888812122424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111
χ511111111111111111111111111111111111111111111111111111111-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1
χ911-1-1-11111-1-1111-1-111-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1111111-1-11-1-1-11111-1-1i−i1-11-111-1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-11-1ii−i−iii−i−i1-1i−ii−i1-1i−ii−ii−i
χ1011-1-1-11111-1-1111-1-111-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1111111-1-11-1-1-11111-1-1i−i1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-11-11ii−i−iii−i−i-11i−i−ii-11i−i−ii−ii
χ1111-1-1-11111-1-1111-1-111-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1111111-1-11-1-1-11111-1-1i−i-111-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-11-11ii−i−iii−i−i-11−iii−i-11−iii−i−ii
χ1211-1-1-11111-1-1111-1-111-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1111111-1-11-1-1-11111-1-1i−i-11-11-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11111111-11-1ii−i−iii−i−i1-1−ii−ii1-1−ii−iii−i
χ1311-1-1-11111-1-1111-1-111-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1111111-1-11-1-1-11111-1-1−ii1-11-111-1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-11-1−i−iii−i−iii1-1−ii−ii1-1−ii−ii−ii
χ1411-1-1-11111-1-1111-1-111-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1111111-1-11-1-1-11111-1-1−ii1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-11-11−i−iii−i−iii-11−iii−i-11−iii−ii−i
χ1511-1-1-11111-1-1111-1-111-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1111111-1-11-1-1-11111-1-1−ii-111-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-11-11−i−iii−i−iii-11i−i−ii-11i−i−iii−i
χ1611-1-1-11111-1-1111-1-111-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1111111-1-11-1-1-11111-1-1−ii-11-11-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11111111-11-1−i−iii−i−iii1-1i−ii−i1-1i−ii−i−ii
χ172222222-12-1-122-1-1-1-1-122222-1-122-1-1-1-12-1-1-1-1-1-122-1-1-1-122-12-1-1-12-1-1-1-1002222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1222200000000-1-10000-1-1000000
χ182222222-12-1-122-1-1-1-1-122222-1-122-1-1-1-12-1-1-1-1-1-122-1-1-1-122-12-1-1-12-1-1-1-10022-2-2-1-1-1-1111122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-2-2-20000000011000011000000
χ192222222-12-1-122-1-1-1-1-122222-1-122-1-1-1-12-1-1-1-1-1-122-1-1-1-122-12-1-1-12-1-1-1-100-2-2221111-1-1-1-1-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-2-2-20000000011000011000000
χ202222222-12-1-122-1-1-1-1-122222-1-122-1-1-1-12-1-1-1-1-1-122-1-1-1-122-12-1-1-12-1-1-1-100-2-2-2-211111111-2-21111-2-21111-2-21111-2-21111222200000000-1-10000-1-1000000
χ21222222-122222-12222222-1-1-12-12-122-1-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1-1-122002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100002-12-1-1-1-1-10000220000-1-100
χ22222222-122222-12222222-1-1-12-12-122-1-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1-1-12200-2-20000-2-2-2-200000000000011111111111100002-12-1-1-1-1-10000-2-200001100
χ23222222-122222-12222222-1-1-12-12-122-1-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-10000-21-2111110000-2-200001100
χ24222222-122222-12222222-1-1-12-12-122-1-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-20000-2-2-2-20000000000001111111111110000-21-2111110000220000-1-100
χ2522222-122222-1222222-1-122-1-12-12-1-122-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1-1-122220022220000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-12-12-1-1-1-100220000-1-10000
χ2622222-122222-1222222-1-122-1-12-12-1-122-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1-1-122-2-200-2-2-2-200001111111111110000000000000000-12-12-1-1-1-100-2-20000110000
χ2722222-122222-1222222-1-122-1-12-12-1-122-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2220022220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000001-21-2111100-2-20000110000
χ2822222-122222-1222222-1-122-1-12-12-1-122-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200-2-2-2-2000011111111111100000000000000001-21-2111100220000-1-10000
χ292222-2222-2-2-222222-2-22222222-2-2-2-2-2-22222222-2-2-2-2-2-2222-2-2-22-2-2-222000000000000000000000000000000000000002-2-22000000002-20000-22000000
χ302222-2222-2-2-222222-2-22222222-2-2-2-2-2-22222222-2-2-2-2-2-2222-2-2-22-2-2-22200000000000000000000000000000000000000-222-200000000-2200002-2000000
χ312222-222-1-21122-1-1-11122222-1-1-2-211112-1-1-1-1-1-1-2-2111122-1-211-1-211-1-10000003−33−33−33−30033−3−30033−3−30033−3−30033−3−32-2-2200000000-1100001-1000000
χ322222-222-1-21122-1-1-11122222-1-1-2-211112-1-1-1-1-1-1-2-2111122-1-211-1-211-1-10000003−33−3−33−330033−3−30033−3−300−3−33300−3−333-222-2000000001-10000-11000000
χ332222-222-1-21122-1-1-11122222-1-1-2-211112-1-1-1-1-1-1-2-2111122-1-211-1-211-1-1000000−33−333−33−300−3−33300−3−3330033−3−30033−3−3-222-2000000001-10000-11000000
χ342222-222-1-21122-1-1-11122222-1-1-2-211112-1-1-1-1-1-1-2-2111122-1-211-1-211-1-1000000−33−33−33−3300−3−33300−3−33300−3−33300−3−3332-2-2200000000-1100001-1000000
χ3522-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-20000000000000000000000000000000000000022-2-200000000220000-2-2000000
χ3622-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-200000000000000000000000000000000000000-2-22200000000-2-2000022000000
χ3722-2-2222-1-2-1-122-11111-2-2-2-22-1-122-1-1-1-12-1-11111-2-21111-2-2-12-1-1-1-211110000003−3−333−3−330033−3−300−3−3330033−3−300−3−33322-2-200000000-1-1000011000000
χ3822-2-2222-1-2-1-122-11111-2-2-2-22-1-122-1-1-1-12-1-11111-2-21111-2-2-12-1-1-1-211110000003−3−33−333−30033−3−300−3−33300−3−3330033−3−3-2-22200000000110000-1-1000000
χ3922-2-2222-1-2-1-122-11111-2-2-2-22-1-122-1-1-1-12-1-11111-2-21111-2-2-12-1-1-1-21111000000−333−33−3−3300−3−3330033−3−30033−3−300−3−333-2-22200000000110000-1-1000000
χ4022-2-2222-1-2-1-122-11111-2-2-2-22-1-122-1-1-1-12-1-11111-2-21111-2-2-12-1-1-1-21111000000−333−3−333−300−3−3330033−3−300−3−3330033−3−322-2-200000000-1-1000011000000
χ4122-2-2-222-121122-111-1-1-2-2-2-22-1-1-2-211112-1-1111122-1-1-1-1-2-2-1-211-12-1-111002-22-2-1-111-1-11122-1-1-1-1-2-2111122-1-1-1-1-2-211112-22-200000000-110000-11000000
χ4222-2-2-222-121122-111-1-1-2-2-2-22-1-1-2-211112-1-1111122-1-1-1-1-2-2-1-211-12-1-111002-2-22-1-11111-1-122-1-1-1-1-2-21111-2-2111122-1-1-1-1-22-22000000001-100001-1000000
χ4322-2-2-222-121122-111-1-1-2-2-2-22-1-1-2-211112-1-1111122-1-1-1-1-2-2-1-211-12-1-11100-222-211-1-1-1-111-2-2111122-1-1-1-122-1-1-1-1-2-21111-22-22000000001-100001-1000000
χ4422-2-2-222-121122-111-1-1-2-2-2-22-1-1-2-211112-1-1111122-1-1-1-1-2-2-1-211-12-1-11100-22-2211-1-111-1-1-2-2111122-1-1-1-1-2-2111122-1-1-1-12-22-200000000-110000-11000000
χ4522-2-2-22-122-2-22-12-2-222-2-211-12-1-21-2-211-12-1-2-2112-122-1-111-1111-1-1-1-1112i−2i002-2000022-2-2000000000000-1-1-1-1-1-111111100002i−i−2ii−i−iii00002i−2i0000−ii00
χ4622-2-2-22-122-2-22-12-2-222-2-211-12-1-21-2-211-12-1-2-2112-122-1-111-1111-1-1-1-1112i−2i00-220000-2-222000000000000111111-1-1-1-1-1-100002i−i−2ii−i−iii0000−2i2i0000i−i00
χ4722-2-2-22-122-2-22-12-2-222-2-211-12-1-21-2-211-12-1-2-2112-122-1-111-1111-1-1-1-111−2i2i002-2000022-2-2000000000000-1-1-1-1-1-11111110000−2ii2i−iii−i−i0000−2i2i0000i−i00
χ4822-2-2-22-122-2-22-12-2-222-2-211-12-1-21-2-211-12-1-2-2112-122-1-111-1111-1-1-1-111−2i2i00-220000-2-222000000000000111111-1-1-1-1-1-10000−2ii2i−iii−i−i00002i−2i0000−ii00
χ4922-2-2-2-1222-2-2-122-2-22211-2-2-1-121-211-2-2-1-1211-2-2-12-1-12211-1111-1-1-1-1112i−2i2-20022-2-20000-1-1-1-1-1-11111110000000000000000−i2ii−2i−i−iii002i−2i0000−ii0000
χ5022-2-2-2-1222-2-2-122-2-22211-2-2-1-121-211-2-2-1-1211-2-2-12-1-12211-1111-1-1-1-1112i−2i-2200-2-2220000111111-1-1-1-1-1-10000000000000000−i2ii−2i−i−iii00−2i2i0000i−i0000
χ5122-2-2-2-1222-2-2-122-2-22211-2-2-1-121-211-2-2-1-1211-2-2-12-1-12211-1111-1-1-1-111−2i2i2-20022-2-20000-1-1-1-1-1-11111110000000000000000i−2i−i2iii−i−i00−2i2i0000i−i0000
χ5222-2-2-2-1222-2-2-122-2-22211-2-2-1-121-211-2-2-1-1211-2-2-12-1-12211-1111-1-1-1-111−2i2i-2200-2-2220000111111-1-1-1-1-1-10000000000000000i−2i−i2iii−i−i002i−2i0000−ii0000
χ53444444-2-24-2-24-2-2-2-2-2-244-2-2-2-214-2-2-211-2-21-2-2114-2-2-211-2-21-2111-211110000440000-2-2-2-2000000000000-2-21111-2-2111100000000000000000000000000
χ54444444-2-24-2-24-2-2-2-2-2-244-2-2-2-214-2-2-211-2-21-2-2114-2-2-211-2-21-2111-211110000-4-40000222200000000000022-1-1-1-122-1-1-1-100000000000000000000000000
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χ5844444-2-24444-2-244444-2-2-2-21-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2111111111111-4-400000000000000000000000000000000000000002222-1-1-1-100000000000000
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χ664444-4-2-24-4-4-4-2-2444-4-4-2-2-2-21-2-22222221-2-2-2-2-2-2222222111-1-1-11-1-1-1110000000000000000000000000000000000000000000000-33-3300000000000000
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χ7144-4-44-24-2-4-2-2-24-2222222-4-4-21-2-2411-2-2-21-2-1-1222-4-1-122221-21112-1-1-1-100000023−23−2323000000−3−3330033−3−300000000000000000000000000000000000000
χ7244-4-44-24-2-4-2-2-24-2222222-4-4-21-2-2411-2-2-21-2-1-1222-4-1-122221-21112-1-1-1-1000000−232323−2300000033−3−300−3−33300000000000000000000000000000000000000
χ7344-4-44-2-24-444-2-24-4-4-4-422221-2-2-2-2-2-2-2-21-2-22222222222-1-111111-1-1-1-1-100000000000000000000000000000000000000000000003i−3i−3i3i00000000000000
χ7444-4-44-2-24-444-2-24-4-4-4-422221-2-2-2-2-2-2-2-21-2-22222222222-1-111111-1-1-1-1-10000000000000000000000000000000000000000000000−3i3i3i−3i00000000000000
χ7544-4-4-44-2-24224-2-222-2-2-4-422-2-21-4222-1-1-2-2122-1-14-2-2-2112212-1-11-211-1-100004-40000-2-222000000000000-2-2111122-1-1-1-100000000000000000000000000
χ7644-4-4-44-2-24224-2-222-2-2-4-422-2-21-4222-1-1-2-2122-1-14-2-2-2112212-1-11-211-1-10000-44000022-2-200000000000022-1-1-1-1-2-2111100000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.