Finite Group Databasebeta

← Group #13155748

Character table — Group #13155748

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222222244444444444444444444444488888888881212121212121212121212121212121212121212121212121212121212121212121212121212181818182424242424242424363636363636363672727272108108
order12442333466666121212121212121233366666666612121212121212121212121236666121212121224448812121212121212121212121212121212242424242424242424242424242424248888666612121212248824242424612242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111111111111111111111111111111-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
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
χ911-1-1-111111-1-111-1-111-1-1-1-1111-1-1-111-1-1-11111-1-1-1-1-1-11111-1-1-11111-1-11-1i−i1-1ii−i−iiiiiii−i−i−i−i−i−i11-1-1111111-1-1-1-1-1-1ii−i−i1111-1-1-1-11-1i−iii−i−i1-1i−ii−i
χ1011-1-1-111111-1-111-1-111-1-1-1-1111-1-1-111-1-1-11111-1-1-1-1-1-11111-1-1-11111-1-11-1i−i-11ii−i−iiiiiii−i−i−i−i−i−i-1-111-1-1-1-1-1-1111111−i−iii1111-1-1-1-1-11i−i−i−iii-11i−i−ii
χ1111-1-1-111111-1-111-1-111-1-1-1-1111-1-1-111-1-1-11111-1-1-1-1-1-11111-1-1-11111-1-11-1−ii1-1−i−iii−i−i−i−i−i−iiiiiii11-1-1111111-1-1-1-1-1-1−i−iii1111-1-1-1-11-1−ii−i−iii1-1−ii−ii
χ1211-1-1-111111-1-111-1-111-1-1-1-1111-1-1-111-1-1-11111-1-1-1-1-1-11111-1-1-11111-1-11-1−ii-11−i−iii−i−i−i−i−i−iiiiiii-1-111-1-1-1-1-1-1111111ii−i−i1111-1-1-1-1-11−iiii−i−i-11−iii−i
χ1311-1-1-111111-1-111-1-111-1-1-1-1111-1-1-111-1-1-11111-1-1-1-1-1-11111-1-1-11111-1-1-11i−i1-1ii−i−iiiiiii−i−i−i−i−i−i11-1-1111111-1-1-1-1-1-1ii−i−i-1-1-1-11111-11−iiii−i−i-11−ii−ii
χ1411-1-1-111111-1-111-1-111-1-1-1-1111-1-1-111-1-1-11111-1-1-1-1-1-11111-1-1-11111-1-1-11i−i-11ii−i−iiiiiii−i−i−i−i−i−i-1-111-1-1-1-1-1-1111111−i−iii-1-1-1-111111-1−ii−i−iii1-1−iii−i
χ1511-1-1-111111-1-111-1-111-1-1-1-1111-1-1-111-1-1-11111-1-1-1-1-1-11111-1-1-11111-1-1-11−ii1-1−i−iii−i−i−i−i−i−iiiiiii11-1-1111111-1-1-1-1-1-1−i−iii-1-1-1-11111-11i−i−i−iii-11i−ii−i
χ1611-1-1-111111-1-111-1-111-1-1-1-1111-1-1-111-1-1-11111-1-1-1-1-1-11111-1-1-11111-1-1-11−ii-11−i−iii−i−i−i−i−i−iiiiiii-1-111-1-1-1-1-1-1111111ii−i−i-1-1-1-111111-1i−iii−i−i1-1i−i−ii
χ172222222-122222-1-1-12222222-1-1-1-1-12-1222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122002200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-100002-1-1-12-1-1-122000000-1-10000
χ182222222-122222-1-1-12222222-1-1-1-1-12-1222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12200-2-20000000000000000-2-2-2-211111111111100002-1-1-12-1-1-1-2-2000000110000
χ192222222-122222-1-1-12222222-1-1-1-1-12-1222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2002200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-10000-2111-2111-2-2000000110000
χ202222222-122222-1-1-12222222-1-1-1-1-12-1222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-20000000000000000-2-2-2-21111111111110000-2111-211122000000-1-10000
χ21222222-122222-12222222-1-1-12-1222-12-1-1-1-1-1-1-1-1-122-1-1222-1-1-1-1-1-1-1-1-1-12222002222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000-12-1-1-12-1-10022000000-1-100
χ22222222-122222-12222222-1-1-12-1222-12-1-1-1-1-1-1-1-1-122-1-1222-1-1-1-1-1-1-1-1-1-122-2-200-2-2-2-211111111111100000000000000000000-12-1-1-12-1-100-2-20000001100
χ23222222-122222-12222222-1-1-12-1222-12-1-1-1-1-1-1-1-1-122-1-1222-1-1-1-1-1-1-1-1-1-1-2-222002222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000001-2111-21100-2-20000001100
χ24222222-122222-12222222-1-1-12-1222-12-1-1-1-1-1-1-1-1-122-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-200-2-2-2-2111111111111000000000000000000001-2111-2110022000000-1-100
χ2522222-1222-1-1-12222-1-1-1-122-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-12-1-1-12-1-1-1-1002222-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222000000000000-1-1-1-1000000
χ2622222-1222-1-1-12222-1-1-1-122-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-12-1-1-12-1-1-1-10022-2-2-1-1-1-122-1-1-1-122-1-1-1-11111-2-21111-2-21111-2-2-2-20000000000001111000000
χ2722222-1222-1-1-12222-1-1-1-122-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-12-1-1-12-1-1-1-100-2-2221111-2-21111-2-21111-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-20000000000001111000000
χ2822222-1222-1-1-12222-1-1-1-122-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-12-1-1-12-1-1-1-100-2-2-2-21111-2-21111-2-211111111-2-21111-2-211112222000000000000-1-1-1-1000000
χ292222-2222-22-2-22222-2-22222222-2-2-222-2-2-22-2-2-2222222-2-2-22-2-2-22-2-2-222000000000000000000000000000000000000002-22-20000000000002-22-2000000
χ302222-2222-22-2-22222-2-22222222-2-2-222-2-2-22-2-2-2222222-2-2-22-2-2-22-2-2-22200000000000000000000000000000000000000-22-22000000000000-22-22000000
χ312222-2-122-2-111222211-1-122-1-12-211-1-1-2112-211-1-1-1-122-211-1-211-1-211-1-10000003−33−30033−3−30033−3−33−33−30033−3−30033−3−32-22-2000000000000-11-11000000
χ322222-2-122-2-111222211-1-122-1-12-211-1-1-2112-211-1-1-1-122-211-1-211-1-211-1-10000003−33−30033−3−30033−3−3−33−3300−3−33300−3−333-22-220000000000001-11-1000000
χ332222-2-122-2-111222211-1-122-1-12-211-1-1-2112-211-1-1-1-122-211-1-211-1-211-1-1000000−33−3300−3−33300−3−3333−33−30033−3−30033−3−3-22-220000000000001-11-1000000
χ342222-2-122-2-111222211-1-122-1-12-211-1-1-2112-211-1-1-1-122-211-1-211-1-211-1-1000000−33−3300−3−33300−3−333−33−3300−3−33300−3−3332-22-2000000000000-11-11000000
χ3522-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-2000000000000000000000000000000000000002i−2i−2i2i0000000000002i−2i−2i2i000000
χ3622-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-200000000000000000000000000000000000000−2i2i2i−2i000000000000−2i2i2i−2i000000
χ3722-2-22-122-2-1-1-122-2-21111-2-2-1-122-1-1-1-12-1-12-2111111-2-2-211-12-1-1-1-21111000000−i3i3i3−i300−i3−i3i3i300i3i3−i3−i33−3−330033−3−300−3−333−2i2i2i−2i000000000000i−i−ii000000
χ3822-2-22-122-2-1-1-122-2-21111-2-2-1-122-1-1-1-12-1-12-2111111-2-2-211-12-1-1-1-21111000000−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3−333−300−3−3330033−3−32i−2i−2i2i000000000000−iii−i000000
χ3922-2-22-122-2-1-1-122-2-21111-2-2-1-122-1-1-1-12-1-12-2111111-2-2-211-12-1-1-1-21111000000i3−i3−i3i300i3i3−i3−i300−i3−i3i3i33−3−330033−3−300−3−3332i−2i−2i2i000000000000−iii−i000000
χ4022-2-22-122-2-1-1-122-2-21111-2-2-1-122-1-1-1-12-1-12-2111111-2-2-211-12-1-1-1-21111000000i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3−333−300−3−3330033−3−3−2i2i2i−2i000000000000i−i−ii000000
χ4122-2-2-222-122-2-22-11122-2-2-2-22-1-11112-1-2-2-2-1222-2-21111-1-1-1-1111-1-1-1-1112-2002-2000000000000000022-2-2-1-1-1-1-1-111111100002-1-1-1-21112-2000000-110000
χ4222-2-2-222-122-2-22-11122-2-2-2-22-1-11112-1-2-2-2-1222-2-21111-1-1-1-1111-1-1-1-1112-200-220000000000000000-2-222111111-1-1-1-1-1-100002-1-1-1-2111-220000001-10000
χ4322-2-2-222-122-2-22-11122-2-2-2-22-1-11112-1-2-2-2-1222-2-21111-1-1-1-1111-1-1-1-111-22002-2000000000000000022-2-2-1-1-1-1-1-11111110000-21112-1-1-1-220000001-10000
χ4422-2-2-222-122-2-22-11122-2-2-2-22-1-11112-1-2-2-2-1222-2-21111-1-1-1-1111-1-1-1-111-2200-220000000000000000-2-222111111-1-1-1-1-1-10000-21112-1-1-12-2000000-110000
χ4522-2-2-22-1222-2-2-12-2-222-2-211-12-1-2-2-2-12111-1-1-1-111-2-211222-1111-1-1-1-1112-22i−2i002i2i−2i−2i−i−i−i−i−i−iiiiiii00000000000000000000-12-1-11-211002i−2i000000−ii00
χ4622-2-2-22-1222-2-2-12-2-222-2-211-12-1-2-2-2-12111-1-1-1-111-2-211222-1111-1-1-1-1112-2−2i2i00−2i−2i2i2iiiiiii−i−i−i−i−i−i00000000000000000000-12-1-11-21100−2i2i000000i−i00
χ4722-2-2-22-1222-2-2-12-2-222-2-211-12-1-2-2-2-12111-1-1-1-111-2-211222-1111-1-1-1-111-222i−2i002i2i−2i−2i−i−i−i−i−i−iiiiiii000000000000000000001-211-12-1-100−2i2i000000i−i00
χ4822-2-2-22-1222-2-2-12-2-222-2-211-12-1-2-2-2-12111-1-1-1-111-2-211222-1111-1-1-1-111-22−2i2i00−2i−2i2i2iiiiiii−i−i−i−i−i−i000000000000000000001-211-12-1-1002i−2i000000−ii00
χ4922-2-2-2-1222-11122-2-2-1-111-2-2-1-12-211-1-1-21122-1-11111-2-22-1-1-1-211-12-1-111002i−2i2-2−i−iii2i2i−i−i−i−i−2i−2iiiii-1-11122-1-1-1-1-2-211112i2i−2i−2i000000000000−i−iii000000
χ5022-2-2-2-1222-11122-2-2-1-111-2-2-1-12-211-1-1-21122-1-11111-2-22-1-1-1-211-12-1-111002i−2i-22−i−iii2i2i−i−i−i−i−2i−2iiiii11-1-1-2-2111122-1-1-1-1−2i−2i2i2i000000000000ii−i−i000000
χ5122-2-2-2-1222-11122-2-2-1-111-2-2-1-12-211-1-1-21122-1-11111-2-22-1-1-1-211-12-1-11100−2i2i2-2ii−i−i−2i−2iiiii2i2i−i−i−i−i-1-11122-1-1-1-1-2-21111−2i−2i2i2i000000000000ii−i−i000000
χ5222-2-2-2-1222-11122-2-2-1-111-2-2-1-12-211-1-1-21122-1-11111-2-22-1-1-1-211-12-1-11100−2i2i-22ii−i−i−2i−2iiiii2i2i−i−i−i−i11-1-1-2-2111122-1-1-1-12i2i−2i−2i000000000000−i−iii000000
χ53444444-2-24444-2-2-2-24444-2-2-2-21-2-2-2-2-2-2-2-21-2-2-2-2-2-2-211-2-2-21111111111440000000000000000000000000000000000000000-2-211-2-21100000000000000
χ54444444-2-24444-2-2-2-24444-2-2-2-21-2-2-2-2-2-2-2-21-2-2-2-2-2-2-211-2-2-21111111111-4-4000000000000000000000000000000000000000022-1-122-1-100000000000000
χ5544444-24-24-2-2-24-2-2-2-2-2-2-244-21-2-211-214-2-2-24-2-2-2-211-2-2-2111-2111-211110000440000000000000000-2-2-2-2-2-21111-2-2111100000000000000000000000000
χ5644444-24-24-2-2-24-2-2-2-2-2-2-244-21-2-211-214-2-2-24-2-2-2-211-2-2-2111-2111-211110000-4-40000000000000000222222-1-1-1-122-1-1-1-100000000000000000000000000
χ5744444-2-244-2-2-2-2444-2-2-2-2-2-21-2-24-2-21-2-211-2-21111-2-2-2-24-2-21-2111-21111004400-2-2-2-2-2-21111-2-21111000000000000000000000000000000000000000000
χ5844444-2-244-2-2-2-2444-2-2-2-2-2-21-2-24-2-21-2-211-2-21111-2-2-2-24-2-21-2111-2111100-4-400222222-1-1-1-122-1-1-1-1000000000000000000000000000000000000000000
χ594444-444-2-44-4-44-2-2-2-4-444444-2-22224-2-4-4-4-2-4-4-444-2-2-2-2222-2222-2222-2-20000000000000000000000000000000000000000000000000000000000000000
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χ614444-44-2-2-44-4-4-2-2-2-2-4-444-2-2-2-21222-2-22221222-2-2-2-2112221-1-1-11-1-1-111000000000000000000000000000000000000000000003-3003-300000000000000
χ624444-44-2-2-44-4-4-2-2-2-2-4-444-2-2-2-21222-2-22221222-2-2-2-2112221-1-1-11-1-1-11100000000000000000000000000000000000000000000-3300-3300000000000000
χ634444-4-24-2-4-2224-2-2-222-2-244-21-22-1-1-21-422-2-422-2-211-2-22-1-112-1-112-1-111000000000000000000000023−2323−2300−3−33300−3−33300000000000000000000000000
χ644444-4-24-2-4-2224-2-2-222-2-244-21-22-1-1-21-422-2-422-2-211-2-22-1-112-1-112-1-1110000000000000000000000−2323−23230033−3−30033−3−300000000000000000000000000
χ654444-4-2-24-4-222-244422-2-2-2-21-2-2-4221-22-1-1-22-1-111-2-2-2-2-42212-1-112-1-11100000023−2323−2300−3−33300−3−333000000000000000000000000000000000000000000
χ664444-4-2-24-4-222-244422-2-2-2-21-2-2-4221-22-1-1-22-1-111-2-2-2-2-42212-1-112-1-111000000−2323−23230033−3−30033−3−3000000000000000000000000000000000000000000
χ6744-4-4444-2-44444-222-4-4-4-4-4-44-2-2-2-2-24-2444-2-4-4-4-4-42222222-2-2-2-2-2222220000000000000000000000000000000000000000000000000000000000000000
χ6844-4-444-24-4444-24-4-4-4-4-4-422-24-2444-24-2-2-2-222222-4-422-4-4-4-2-2-2-2-2222220000000000000000000000000000000000000000000000000000000000000000
χ6944-4-444-2-2-4444-2-222-4-4-4-422-2-21-2-2-2-2-2-2-2-212222222-1-122211111-1-1-1-1-1000000000000000000000000000000000000000000003-300-3300000000000000
χ7044-4-444-2-2-4444-2-222-4-4-4-422-2-21-2-2-2-2-2-2-2-212222222-1-122211111-1-1-1-1-100000000000000000000000000000000000000000000-33003-300000000000000
χ7144-4-44-24-2-4-2-2-24-2222222-4-4-21-2-211-214-2-2-2-42222-1-1222-1-11-21112-1-1-1-1000000000000000000000023−23−232300−3−3330033−3−300000000000000000000000000
χ7244-4-44-24-2-4-2-2-24-2222222-4-4-21-2-211-214-2-2-2-42222-1-1222-1-11-21112-1-1-1-10000000000000000000000−232323−230033−3−300−3−33300000000000000000000000000
χ7344-4-44-2-24-4-2-2-2-24-4-42222221-2-24-2-21-2-211-22-1-1-1-12222-4221-21112-1-1-1-1000000−2i32i32i3−2i300i3i3−i3−i300−i3−i3i3i3000000000000000000000000000000000000000000
χ7444-4-44-2-24-4-2-2-2-24-4-42222221-2-24-2-21-2-211-22-1-1-1-12222-4221-21112-1-1-1-10000002i3−2i3−2i32i300−i3−i3i3i300i3i3−i3−i3000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.