Finite Group Databasebeta

← Group #13155435

Character table — Group #13155435

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222222244444444444444444444444488888888881212121212121212121212121212121212121212121212121212121212121212121212121212181818182424242424242424363636363636363672727272108108
order1244233346666612121212121212123336666666661212121212121212121212123666612121212122444441212121212121212121212121212121212121212121212121212121212121212224466661212121266888812122424242424
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
χ911-1-1-1111111-1-1111-1-1-1-1-1-111111-1-1-1-1-1-11111111-1-1-1-1-1-11-1-1-11111-1-11-1i−ii−iii−i−iii−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i1-11-11111-1-1-1-11-1i−ii−i1-1i−ii−i1-1
χ1011-1-1-1111111-1-1111-1-1-1-1-1-111111-1-1-1-1-1-11111111-1-1-1-1-1-11-1-1-11111-1-11-1i−i−iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-11-111111-1-1-1-1-11i−i−ii-11i−i−ii-11
χ1111-1-1-1111111-1-1111-1-1-1-1-1-111111-1-1-1-1-1-11111111-1-1-1-1-1-11-1-1-11111-1-11-1−iii−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-11-111111-1-1-1-1-11−iii−i-11−iii−i-11
χ1211-1-1-1111111-1-1111-1-1-1-1-1-111111-1-1-1-1-1-11111111-1-1-1-1-1-11-1-1-11111-1-11-1−ii−ii−i−iii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii1-11-11111-1-1-1-11-1−ii−ii1-1−ii−ii1-1
χ1311-1-1-1111111-1-1111-1-1-1-1-1-111111-1-1-1-1-1-11111111-1-1-1-1-1-11-1-1-11111-1-1-11i−ii−iii−i−iii−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i1-11-1-1-1-1-111111-1−ii−ii1-1−ii−ii-11
χ1411-1-1-1111111-1-1111-1-1-1-1-1-111111-1-1-1-1-1-11111111-1-1-1-1-1-11-1-1-11111-1-1-11i−i−iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-11-11-1-1-1-11111-11−iii−i-11−iii−i1-1
χ1511-1-1-1111111-1-1111-1-1-1-1-1-111111-1-1-1-1-1-11111111-1-1-1-1-1-11-1-1-11111-1-1-11−iii−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-11-11-1-1-1-11111-11i−i−ii-11i−i−ii1-1
χ1611-1-1-1111111-1-1111-1-1-1-1-1-111111-1-1-1-1-1-11111111-1-1-1-1-1-11-1-1-11111-1-1-11−ii−ii−i−iii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii1-11-1-1-1-1-111111-1i−ii−i1-1i−ii−i-11
χ172222222-1222-1-1-1-1-1-1-12222-1-12-1-122-1-1-1-1222-1-1-1-1-1-1-1-122-12-1-1-12-1-1-1-1002222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-1222200000000-1-10000-1-1000000
χ182222222-1222-1-1-1-1-1-1-12222-1-12-1-122-1-1-1-1222-1-1-1-1-1-1-1-122-12-1-1-12-1-1-1-10022-2-2-1-1-1-1111122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-2-2-20000000011000011000000
χ192222222-1222-1-1-1-1-1-1-12222-1-12-1-122-1-1-1-1222-1-1-1-1-1-1-1-122-12-1-1-12-1-1-1-100-2-2221111-1-1-1-1-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-2-2-20000000011000011000000
χ202222222-1222-1-1-1-1-1-1-12222-1-12-1-122-1-1-1-1222-1-1-1-1-1-1-1-122-12-1-1-12-1-1-1-100-2-2-2-211111111-2-21111-2-21111-2-21111-2-21111222200000000-1-10000-1-1000000
χ21222222-1222-1222222222-1-12-1-12-12-122-1-1-12-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-122002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100002-1-1-12-1-1-10000220000-1-100
χ22222222-1222-1222222222-1-12-1-12-12-122-1-1-12-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-12200-2-20000-2-2-2-200000000000011111111111100002-1-1-12-1-1-10000-2-200001100
χ23222222-1222-1222222222-1-12-1-12-12-122-1-1-12-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-10000-2111-21110000-2-200001100
χ24222222-1222-1222222222-1-12-1-12-12-122-1-1-12-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-20000-2-2-2-20000000000001111111111110000-2111-21110000220000-1-100
χ2522222-1222-122222222-1-122-12-1-12-12-1-122-1-12-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-122220022220000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-12-1-1-12-1-100220000-1-10000
χ2622222-1222-122222222-1-122-12-1-12-12-1-122-1-12-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-122-2-200-2-2-2-200001111111111110000000000000000-12-1-1-12-1-100-2-20000110000
χ2722222-1222-122222222-1-122-12-1-12-12-1-122-1-12-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2220022220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000001-2111-21100-2-20000110000
χ2822222-1222-122222222-1-122-12-1-12-12-1-122-1-12-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200-2-2-2-2000011111111111100000000000000001-2111-21100220000-1-10000
χ292222-2222-222-2-22-2-222222222222-2-2-2-2-2-22-2-2-2-2-2-22222222-2-2-22-2-2-222000000000000000000000000000000000000002-2-22000000002-20000-22000000
χ302222-2222-222-2-22-2-222222222222-2-2-2-2-2-22-2-2-2-2-2-22222222-2-2-22-2-2-22200000000000000000000000000000000000000-222-200000000-2200002-2000000
χ312222-222-1-22211-111-1-12222-1-12-1-1-2-211112-2-21111-1-1-1-122-1-211-1-211-1-10000003−33−33−33−30033−3−30033−3−30033−3−30033−3−32-2-2200000000-1100001-1000000
χ322222-222-1-22211-111-1-12222-1-12-1-1-2-211112-2-21111-1-1-1-122-1-211-1-211-1-10000003−33−3−33−330033−3−30033−3−300−3−33300−3−333-222-2000000001-10000-11000000
χ332222-222-1-22211-111-1-12222-1-12-1-1-2-211112-2-21111-1-1-1-122-1-211-1-211-1-1000000−33−333−33−300−3−33300−3−3330033−3−30033−3−3-222-2000000001-10000-11000000
χ342222-222-1-22211-111-1-12222-1-12-1-1-2-211112-2-21111-1-1-1-122-1-211-1-211-1-1000000−33−33−33−3300−3−33300−3−33300−3−33300−3−3332-2-2200000000-1100001-1000000
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
χ3722-2-2222-1-222-1-1-11111-2-2-2-2-1-12-1-122-1-1-1-12-2-211111111-2-2-12-1-1-1-21111000000−i3i3i3−i3−i3i3i3−i300−i3−i3i3i300i3i3−i3−i300−i3−i3i3i300i3i3−i3−i322-2-200000000-1-1000011000000
χ3822-2-2222-1-222-1-1-11111-2-2-2-2-1-12-1-122-1-1-1-12-2-211111111-2-2-12-1-1-1-21111000000−i3i3i3−i3i3−i3−i3i300−i3−i3i3i300i3i3−i3−i300i3i3−i3−i300−i3−i3i3i3-2-22200000000110000-1-1000000
χ3922-2-2222-1-222-1-1-11111-2-2-2-2-1-12-1-122-1-1-1-12-2-211111111-2-2-12-1-1-1-21111000000i3−i3−i3i3−i3i3i3−i300i3i3−i3−i300−i3−i3i3i300−i3−i3i3i300i3i3−i3−i3-2-22200000000110000-1-1000000
χ4022-2-2222-1-222-1-1-11111-2-2-2-2-1-12-1-122-1-1-1-12-2-211111111-2-2-12-1-1-1-21111000000i3−i3−i3i3i3−i3−i3i300i3i3−i3−i300−i3−i3i3i300i3i3−i3−i300−i3−i3i3i322-2-200000000-1-1000011000000
χ4122-2-2-222-122211-1-1-111-2-2-2-2-1-12-1-1-2-21111222-1-1-1-11111-2-2-1-211-12-1-111002i−2i2i−2i−i−iii−i−iii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2-22-200000000-110000-11000000
χ4222-2-2-222-122211-1-1-111-2-2-2-2-1-12-1-1-2-21111222-1-1-1-11111-2-2-1-211-12-1-111002i−2i−2i2i−i−iiiii−i−i2i2i−i−i−i−i−2i−2iiiii−2i−2iiiii2i2i−i−i−i−i-22-22000000001-100001-1000000
χ4322-2-2-222-122211-1-1-111-2-2-2-2-1-12-1-1-2-21111222-1-1-1-11111-2-2-1-211-12-1-11100−2i2i2i−2iii−i−i−i−iii−2i−2iiiii2i2i−i−i−i−i2i2i−i−i−i−i−2i−2iiiii-22-22000000001-100001-1000000
χ4422-2-2-222-122211-1-1-111-2-2-2-2-1-12-1-1-2-21111222-1-1-1-11111-2-2-1-211-12-1-11100−2i2i−2i2iii−i−iii−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i2-22-200000000-110000-11000000
χ4522-2-2-22-1222-1-2-2222-2-2-2-2112-1-12-1-21-2-211-12-122-1-1-2-21111-1111-1-1-1-1112-2002i−2i00002i2i−2i−2i000000000000−i−i−i−i−i−iiiiiii00002-1-1-1-211100002i−2i0000−ii00
χ4622-2-2-22-1222-1-2-2222-2-2-2-2112-1-12-1-21-2-211-12-122-1-1-2-21111-1111-1-1-1-1112-200−2i2i0000−2i−2i2i2i000000000000iiiiii−i−i−i−i−i−i00002-1-1-1-21110000−2i2i0000i−i00
χ4722-2-2-22-1222-1-2-2222-2-2-2-2112-1-12-1-21-2-211-12-122-1-1-2-21111-1111-1-1-1-111-22002i−2i00002i2i−2i−2i000000000000−i−i−i−i−i−iiiiiii0000-21112-1-1-10000−2i2i0000i−i00
χ4822-2-2-22-1222-1-2-2222-2-2-2-2112-1-12-1-21-2-211-12-122-1-1-2-21111-1111-1-1-1-111-2200−2i2i0000−2i−2i2i2i000000000000iiiiii−i−i−i−i−i−i0000-21112-1-1-100002i−2i0000−ii00
χ4922-2-2-2-1222-12-2-2222-2-211-2-2-12-1-121-211-2-2-1-12-1-12211-2-211-1111-1-1-1-1112-22i−2i002i2i−2i−2i0000−i−i−i−i−i−iiiiiii0000000000000000-12-1-11-211002i−2i0000−ii0000
χ5022-2-2-2-1222-12-2-2222-2-211-2-2-12-1-121-211-2-2-1-12-1-12211-2-211-1111-1-1-1-1112-2−2i2i00−2i−2i2i2i0000iiiiii−i−i−i−i−i−i0000000000000000-12-1-11-21100−2i2i0000i−i0000
χ5122-2-2-2-1222-12-2-2222-2-211-2-2-12-1-121-211-2-2-1-12-1-12211-2-211-1111-1-1-1-111-222i−2i002i2i−2i−2i0000−i−i−i−i−i−iiiiiii00000000000000001-211-12-1-100−2i2i0000i−i0000
χ5222-2-2-2-1222-12-2-2222-2-211-2-2-12-1-121-211-2-2-1-12-1-12211-2-211-1111-1-1-1-111-22−2i2i00−2i−2i2i2i0000iiiiii−i−i−i−i−i−i00000000000000001-211-12-1-1002i−2i0000−ii0000
χ53444444-2-244-2-2-2-2-2-2-2-244-2-2-21-2-214-2-2-211-24-2-2-211-2-211-2-21-2111-211110000440000-2-2-2-2000000000000-2-21111-2-2111100000000000000000000000000
χ54444444-2-244-2-2-2-2-2-2-2-244-2-2-21-2-214-2-2-211-24-2-2-211-2-211-2-21-2111-211110000-4-40000222200000000000022-1-1-1-122-1-1-1-100000000000000000000000000
χ5544444-24-24-24-2-2-2-2-2-2-2-2-2441-2-21-2-2411-2-2-2-2411-2-211-2-2-2-21-2111-21111004400-2-2-2-20000-2-21111-2-2111100000000000000000000000000000000000000
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χ5744444-2-244-2-24444444-2-2-2-2-2-21-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2111111111111440000000000000000000000000000000000000000-2-211-2-21100000000000000
χ5844444-2-244-2-24444444-2-2-2-2-2-21-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2111111111111-4-4000000000000000000000000000000000000000022-1-122-1-100000000000000
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χ614444-44-2-2-44-222-222-2-244-2-2-21-2-21-4222-1-1-2-4222-1-1-2-211-2-212-1-112-1-1110000000000−2323−23230000000000000033−3−30033−3−300000000000000000000000000
χ624444-4-244-4-24-4-44-4-444-2-244-24-2-242-422-4-4-22-422-4-4-2-244-2-2-2222-2222-2-20000000000000000000000000000000000000000000000000000000000000000
χ634444-4-24-2-4-2422-222-2-2-2-2441-2-21-22-4-1-122-22-4-1-12211-2-2-2-212-1-112-1-11100000023−2323−23000000−3−33300−3−33300000000000000000000000000000000000000
χ644444-4-24-2-4-2422-222-2-2-2-2441-2-21-22-4-1-122-22-4-1-12211-2-2-2-212-1-112-1-111000000−2323−232300000033−3−30033−3−300000000000000000000000000000000000000
χ654444-4-2-24-4-2-2-4-44-4-444-2-2-2-2-2-21-2-22222221222222-2-2-2-2111-1-1-11-1-1-111000000000000000000000000000000000000000000003-3003-300000000000000
χ664444-4-2-24-4-2-2-4-44-4-444-2-2-2-2-2-21-2-22222221222222-2-2-2-2111-1-1-11-1-1-11100000000000000000000000000000000000000000000-3300-3300000000000000
χ6744-4-444-24-44-2444-4-4-4-4-4-4224-2-24-24-244-2-2-2-42-4-422-4-42222-2-2-2-2-2222220000000000000000000000000000000000000000000000000000000000000000
χ6844-4-444-2-2-44-2-2-2-22222-4-422-21-2-214-2-2-211-2-4222-1-122-1-1221-21112-1-1-1-10000000000−2i32i32i3−2i300000000000000i3i3−i3−i300−i3−i3i3i300000000000000000000000000
χ6944-4-444-2-2-44-2-2-2-22222-4-422-21-2-214-2-2-211-2-4222-1-122-1-1221-21112-1-1-1-100000000002i3−2i3−2i32i300000000000000−i3−i3i3i300i3i3−i3−i300000000000000000000000000
χ7044-4-44-244-4-24444-4-4-4-422-4-4-24-2-24-24-2-244-22-422-4-422-4-422-2-2-2-2-2222220000000000000000000000000000000000000000000000000000000000000000
χ7144-4-44-24-2-4-24-2-2-2222222-4-41-2-21-2-2411-2-2-22-4-1-122-1-122221-21112-1-1-1-1000000−2i32i32i3−2i3000000i3i3−i3−i300−i3−i3i3i300000000000000000000000000000000000000
χ7244-4-44-24-2-4-24-2-2-2222222-4-41-2-21-2-2411-2-2-22-4-1-122-1-122221-21112-1-1-1-10000002i3−2i3−2i32i3000000−i3−i3i3i300i3i3−i3−i300000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.