Finite Group Databasebeta

← Group #13155437

Character table — Group #13155437

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222222244444444444444444444444488888888881212121212121212121212121212121212121212121212121212121212121212121212121212181818182424242424242424363636363636363672727272108108
order124423334666661212121212121212333666666666121212121212121212121212366661212121212444488121212121212121212121212121212121212121212121212121212121212121222442424242424242424224466121266121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-1-1-11-11-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-11-1111
χ511111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-11-11-1-1-1-1-11-11-1-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-11-11-111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111
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
χ911-1-1-11111-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1-11111-1-1i−ii−ii−iii−i−iii−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i1-11-1ii−i−iii−i−i11-1-11-11-111-1-1i−i
χ1011-1-1-11111-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1-11111-1-1i−ii−i−iiii−i−iii−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i1-11-1−i−iii−i−iii-1-1111-11-1-1-111−ii
χ1111-1-1-11111-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1-11111-1-1i−i−iii−iii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-11-11ii−i−iii−i−i1-1-11-11-111-1-11−ii
χ1211-1-1-11111-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1-11111-1-1i−i−ii−iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-11-11−i−iii−i−iii-111-1-11-11-111-1i−i
χ1311-1-1-11111-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1-11111-1-1−iii−ii−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-11-11ii−i−iii−i−i-111-1-11-11-111-1−ii
χ1411-1-1-11111-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1-11111-1-1−iii−i−ii−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-11-11−i−iii−i−iii1-1-11-11-111-1-11i−i
χ1511-1-1-11111-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1-11111-1-1−ii−iii−i−i−iii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii1-11-1ii−i−iii−i−i-1-1111-11-1-1-111i−i
χ1611-1-1-11111-1-111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1-11111-1-1−ii−ii−ii−i−iii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii1-11-1−i−iii−i−iii11-1-11-11-111-1-1−ii
χ172222222-122222-1222222-1-12-1-12-1-12-122-1-12-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-100222200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100002-12-1-1-1-1-1020200000-10-100
χ182222222-122222-1222222-1-12-1-12-1-12-122-1-12-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-10022-2-200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-10000-21-2111110-20-20000010100
χ192222222-122222-1222222-1-12-1-12-1-12-122-1-12-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2220000-2-2-2-200000000000011111111111100002-12-1-1-1-1-10-20-20000010100
χ202222222-122222-1222222-1-12-1-12-1-12-122-1-12-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-20000-2-2-2-20000000000001111111111110000-21-211111020200000-10-100
χ21222222-122222-122222-1-122-12-1-12-1-12-1-122-12-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-122002222220000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-12-12-1-1-1-120200000-10-1000
χ22222222-122222-122222-1-122-12-1-12-1-12-1-122-12-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-12200-2-222220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000001-21-21111-20-200000101000
χ23222222-122222-122222-1-122-12-1-12-1-12-1-122-12-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-20022-2-2-2-200001111111111110000000000000000-12-12-1-1-1-1-20-200000101000
χ24222222-122222-122222-1-122-12-1-12-1-12-1-122-12-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-2-2-2000011111111111100000000000000001-21-2111120200000-10-1000
χ2522222-1222-1-1-122-1-1-1-12222-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-12-1-1-12-1-1-1-1222200-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222000000000000-1-1-1-1000000
χ2622222-1222-1-1-122-1-1-1-12222-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-12-1-1-12-1-1-1-122-2-200-1-1-1-1111122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-2-2-20000000000001111000000
χ2722222-1222-1-1-122-1-1-1-12222-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-12-1-1-12-1-1-1-1-2-222001111-1-1-1-1-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-2-2-20000000000001111000000
χ2822222-1222-1-1-122-1-1-1-12222-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-12-1-1-12-1-1-1-1-2-2-2-20011111111-2-21111-2-21111-2-21111-2-211112222000000000000-1-1-1-1000000
χ292222-2222-2-2-2222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222-2-2-22-2-2-222000000000000000000000000000000000000002-2-220000000000002-2-22000000
χ302222-2222-2-2-2222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222-2-2-22-2-2-22200000000000000000000000000000000000000-222-2000000000000-222-2000000
χ312222-2-122-211-12211-1-12222-1-12-1-12-2-21111-2-21111-1-1-1-122-1-211-1-211-1-10000003−33−33−33−30033−3−30033−3−30033−3−30033−3−32-2-22000000000000-111-1000000
χ322222-2-122-211-12211-1-12222-1-12-1-12-2-21111-2-21111-1-1-1-122-1-211-1-211-1-10000003−33−3−33−330033−3−30033−3−300−3−33300−3−333-222-20000000000001-1-11000000
χ332222-2-122-211-12211-1-12222-1-12-1-12-2-21111-2-21111-1-1-1-122-1-211-1-211-1-1000000−33−333−33−300−3−33300−3−3330033−3−30033−3−3-222-20000000000001-1-11000000
χ342222-2-122-211-12211-1-12222-1-12-1-12-2-21111-2-21111-1-1-1-122-1-211-1-211-1-1000000−33−33−33−3300−3−33300−3−33300−3−33300−3−3332-2-22000000000000-111-1000000
χ3522-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-20000000000000000000000000000000000000022-2-200000000000022-2-2000000
χ3622-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-200000000000000000000000000000000000000-2-222000000000000-2-222000000
χ3722-2-22-122-2-1-1-1221111-2-2-2-2-1-12-1-1222-1-1-1-1-2-211111111-2-2-12-1-1-1-21111000000−i3i3i3−i3−i3i3i3−i300−i3−i3i3i300i3i3−i3−i300−i3−i3i3i300i3i3−i3−i322-2-2000000000000-1-111000000
χ3822-2-22-122-2-1-1-1221111-2-2-2-2-1-12-1-1222-1-1-1-1-2-211111111-2-2-12-1-1-1-21111000000−i3i3i3−i3i3−i3−i3i300−i3−i3i3i300i3i3−i3−i300i3i3−i3−i300−i3−i3i3i3-2-22200000000000011-1-1000000
χ3922-2-22-122-2-1-1-1221111-2-2-2-2-1-12-1-1222-1-1-1-1-2-211111111-2-2-12-1-1-1-21111000000i3−i3−i3i3−i3i3i3−i300i3i3−i3−i300−i3−i3i3i300−i3−i3i3i300i3i3−i3−i3-2-22200000000000011-1-1000000
χ4022-2-22-122-2-1-1-1221111-2-2-2-2-1-12-1-1222-1-1-1-1-2-211111111-2-2-12-1-1-1-21111000000i3−i3−i3i3i3−i3−i3i300i3i3−i3−i300−i3−i3i3i300i3i3−i3−i300−i3−i3i3i322-2-2000000000000-1-111000000
χ4122-2-2-222-12-2-222-122-2-2-2-2112-1-12-1-1-21-2-2112-122-1-1-2-21111-1111-1-1-1-111002i−2i2i−2i00002i2i−2i−2i000000000000−i−i−i−i−i−iiiiiii00002i−i−2ii−i−iii020-200000-10100
χ4222-2-2-222-12-2-222-122-2-2-2-2112-1-12-1-1-21-2-2112-122-1-1-2-21111-1111-1-1-1-111002i−2i−2i2i00002i2i−2i−2i000000000000−i−i−i−i−i−iiiiiii0000−2ii2i−iii−i−i0-2020000010-100
χ4322-2-2-222-12-2-222-122-2-2-2-2112-1-12-1-1-21-2-2112-122-1-1-2-21111-1111-1-1-1-11100−2i2i2i−2i0000−2i−2i2i2i000000000000iiiiii−i−i−i−i−i−i00002i−i−2ii−i−iii0-2020000010-100
χ4422-2-2-222-12-2-222-122-2-2-2-2112-1-12-1-1-21-2-2112-122-1-1-2-21111-1111-1-1-1-11100−2i2i−2i2i0000−2i−2i2i2i000000000000iiiiii−i−i−i−i−i−i0000−2ii2i−iii−i−i020-200000-10100
χ4522-2-2-22-122-2-22-1222-2-211-2-2-12-1-12-11-211-2-2-12-1-12211-2-211-1111-1-1-1-1112i−2i002i−2i2i2i−2i−2i0000−i−i−i−i−i−iiiiiii0000000000000000−i2ii−2i−i−iii20-200000-101000
χ4622-2-2-22-122-2-22-1222-2-211-2-2-12-1-12-11-211-2-2-12-1-12211-2-211-1111-1-1-1-1112i−2i00−2i2i2i2i−2i−2i0000−i−i−i−i−i−iiiiiii0000000000000000i−2i−i2iii−i−i-2020000010-1000
χ4722-2-2-22-122-2-22-1222-2-211-2-2-12-1-12-11-211-2-2-12-1-12211-2-211-1111-1-1-1-111−2i2i002i−2i−2i−2i2i2i0000iiiiii−i−i−i−i−i−i0000000000000000−i2ii−2i−i−iii-2020000010-1000
χ4822-2-2-22-122-2-22-1222-2-211-2-2-12-1-12-11-211-2-2-12-1-12211-2-211-1111-1-1-1-111−2i2i00−2i2i−2i−2i2i2i0000iiiiii−i−i−i−i−i−i0000000000000000i−2i−i2iii−i−i20-200000-101000
χ4922-2-2-2-122211-122-1-111-2-2-2-2-1-12-1-12-2-2111122-1-1-1-11111-2-2-1-211-12-1-1112i−2i2i−2i00−i−iii−i−iii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2-22-2000000000000-11-11000000
χ5022-2-2-2-122211-122-1-111-2-2-2-2-1-12-1-12-2-2111122-1-1-1-11111-2-2-1-211-12-1-1112i−2i−2i2i00−i−iiiii−i−i2i2i−i−i−i−i−2i−2iiiii−2i−2iiiii2i2i−i−i−i−i-22-220000000000001-11-1000000
χ5122-2-2-2-122211-122-1-111-2-2-2-2-1-12-1-12-2-2111122-1-1-1-11111-2-2-1-211-12-1-111−2i2i2i−2i00ii−i−i−i−iii−2i−2iiiii2i2i−i−i−i−i2i2i−i−i−i−i−2i−2iiiii-22-220000000000001-11-1000000
χ5222-2-2-2-122211-122-1-111-2-2-2-2-1-12-1-12-2-2111122-1-1-1-11111-2-2-1-211-12-1-111−2i2i−2i2i00ii−i−iii−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i2-22-2000000000000-11-11000000
χ53444444-2-24444-2-24444-2-2-2-2-2-21-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111111111000044000000000000000000000000000000000000-2-2-2-2111100000000000000
χ54444444-2-24444-2-24444-2-2-2-2-2-21-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111111110000-4-40000000000000000000000000000000000002222-1-1-1-100000000000000
χ5544444-24-24-2-2-24-2-2-2-2-244-2-2-21-2-21-24-2-2-2114-2-2-211-2-211-2-21-2111-211110044000000-2-2-2-2000000000000-2-21111-2-2111100000000000000000000000000
χ5644444-24-24-2-2-24-2-2-2-2-244-2-2-21-2-21-24-2-2-2114-2-2-211-2-211-2-21-2111-2111100-4-4000000222200000000000022-1-1-1-122-1-1-1-100000000000000000000000000
χ5744444-2-244-2-2-2-24-2-2-2-2-2-2441-2-21-2-2-2411-2-2-2411-2-211-2-2-2-21-2111-21111440000-2-2-2-20000-2-21111-2-2111100000000000000000000000000000000000000
χ5844444-2-244-2-2-2-24-2-2-2-2-2-2441-2-21-2-2-2411-2-2-2411-2-211-2-2-2-21-2111-21111-4-400002222000022-1-1-1-122-1-1-1-100000000000000000000000000000000000000
χ594444-444-2-4-4-444-2-4-44444-2-24-2-24-2-2-42-4-422-42-4-42244-2-2-2-2-2222-2222-2-20000000000000000000000000000000000000000000000000000000000000000
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χ614444-44-2-2-4-4-44-2-2-4-444-2-2-2-2-2-21-2-21222222222222-2-2-2-2111-1-1-11-1-1-11100000000000000000000000000000000000000000000003-33-300000000000000
χ624444-44-2-2-4-4-44-2-2-4-444-2-2-2-2-2-21-2-21222222222222-2-2-2-2111-1-1-11-1-1-1110000000000000000000000000000000000000000000000-33-3300000000000000
χ634444-4-24-2-422-24-222-2-244-2-2-21-2-21-2-4222-1-1-4222-1-1-2-211-2-212-1-112-1-111000000000023−2323−2300000000000000−3−33300−3−33300000000000000000000000000
χ644444-4-24-2-422-24-222-2-244-2-2-21-2-21-2-4222-1-1-4222-1-1-2-211-2-212-1-112-1-1110000000000−2323−23230000000000000033−3−30033−3−300000000000000000000000000
χ654444-4-2-24-422-2-2422-2-2-2-2441-2-21-2-22-4-1-1222-4-1-12211-2-2-2-212-1-112-1-11100000023−2323−23000000−3−33300−3−33300000000000000000000000000000000000000
χ664444-4-2-24-422-2-2422-2-2-2-2441-2-21-2-22-4-1-1222-4-1-12211-2-2-2-212-1-112-1-111000000−2323−232300000033−3−30033−3−300000000000000000000000000000000000000
χ6744-4-4444-2-44444-2-4-4-4-4-4-4224-2-24-2-24-244-2-2-42-4-422-4-42222-2-2-2-2-2222220000000000000000000000000000000000000000000000000000000000000000
χ6844-4-444-24-4444-24-4-4-4-422-4-4-24-2-24-2-24-2-2442-422-4-422-4-422-2-2-2-2-2222220000000000000000000000000000000000000000000000000000000000000000
χ6944-4-444-2-2-4444-2-2-4-4-4-42222-2-21-2-21-2-2-2-2-2-22222222222-1-111111-1-1-1-1-100000000000000000000000000000000000000000000003i−3i−3i3i00000000000000
χ7044-4-444-2-2-4444-2-2-4-4-4-42222-2-21-2-21-2-2-2-2-2-22222222222-1-111111-1-1-1-1-10000000000000000000000000000000000000000000000−3i3i3i−3i00000000000000
χ7144-4-44-24-2-4-2-2-24-22222-4-422-21-2-21-24-2-2-211-4222-1-122-1-1221-21112-1-1-1-10000000000−2i32i32i3−2i300000000000000i3i3−i3−i300−i3−i3i3i300000000000000000000000000
χ7244-4-44-24-2-4-2-2-24-22222-4-422-21-2-21-24-2-2-211-4222-1-122-1-1221-21112-1-1-1-100000000002i3−2i3−2i32i300000000000000−i3−i3i3i300i3i3−i3−i300000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.