Finite Group Databasebeta

← Group #13155339

Character table — Group #13155339

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1122222222222444444444444444444448888888888888899121212121212121212121212121218181818181818242424242424242424242424242424242424242436363636363672727272108108
order1223334466666333666666666121212121212121236666121212121212121212442244666688121212122241212121266666612121212121224242424242424246688882424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ511111111111111111111111111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1
χ611111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ711111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-111-1-1
χ811111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ9111111-1-111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1111-11-111-1-1i−i11-1-1-1-1111111-111-1-11-111-1-1iiii−i−i−i−i-1-1i−ii−ii−ii−ii−i
χ10111111-1-111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1111-11-111-1-1−ii11-1-1-1-1111111-111-1-11-111-1-1−i−i−i−iiiii-1-1−ii−ii−ii−ii−ii
χ11111111-1-111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-111-11-11-1-111i−i-1-111-1-111111-11-1-111-11-1-111iiii−i−i−i−i-1-1−ii−ii−ii−iii−i
χ12111111-1-111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-111-11-11-1-111−ii-1-111-1-111111-11-1-111-11-1-111−i−i−i−iiiii-1-1i−ii−ii−ii−i−ii
χ13111111-1-111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1i−i-1-11111-1-1-1-1-11-111-1-1-11-1-111iiii−i−i−i−i11i−i−iii−i−ii−ii
χ14111111-1-111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1−ii-1-11111-1-1-1-1-11-111-1-1-11-1-111−i−i−i−iiiii11−iii−i−iii−ii−i
χ15111111-1-111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111i−i11-1-111-1-1-1-1-1-11-1-1111-111-1-1iiii−i−i−i−i11−iii−i−iii−i−ii
χ16111111-1-111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111−ii11-1-111-1-1-1-1-1-11-1-1111-111-1-1−i−i−i−iiiii11i−i−iii−i−iii−i
χ1722222-122-1-122-12-1-122-1-1-1-12-1-1-1-1222222-12-1-1-12-1-1-1-1-1-1-1-1222222-1-1-1-100-1-1-1-1222-1-1-1-122-1-1-1-122-1-1-1-100000000-1-10000000000
χ1822222-122-1-122-12-1-122-1-1-1-12-1-1-1-1222222-12-1-1-12-1-1-1-1-1-1-1-122-2-2-2-21111001111222-1-1-1-1-2-21111-2-2111100000000-1-10000000000
χ1922222-122-1-122-12-1-122-1-1-1-12-1-1-1-1222222-12-1-1-12-1-1-1-1-1-1-1-1-2-222-2-2-1-1-1-1001111-2-2-2111122-1-1-1-1-2-2111100000000110000000000
χ2022222-122-1-122-12-1-122-1-1-1-12-1-1-1-1222222-12-1-1-12-1-1-1-1-1-1-1-1-2-2-2-222111100-1-1-1-1-2-2-21111-2-2111122-1-1-1-100000000110000000000
χ2122222-1-2-2-1-122-12-1-122-1-1-1-12-1-111-2-2-2-2-2-2-12-1-1-1-211111111222-22-2-1-11100-1-111-2-22-1-1-1-12-2-1-1112-2-1-11100000000110000000000
χ2222222-1-2-2-1-122-12-1-122-1-1-1-12-1-111-2-2-2-2-2-2-12-1-1-1-21111111122-22-2211-1-10011-1-1-2-22-1-1-1-1-2211-1-1-2211-1-100000000110000000000
χ2322222-1-2-2-1-122-12-1-122-1-1-1-12-1-111-2-2-2-2-2-2-12-1-1-1-211111111-2-22-2-22-1-1110011-1-122-211112-2-1-111-2211-1-100000000-1-10000000000
χ2422222-1-2-2-1-122-12-1-122-1-1-1-12-1-111-2-2-2-2-2-2-12-1-1-1-211111111-2-2-222-211-1-100-1-11122-21111-2211-1-12-2-1-11100000000-1-10000000000
χ252222-122222-122-12-12-122-1-1-1-1222-12-1-1-12-1-1-1-1-1-1-1-122-1-1-1-100220022222200000000000-1-1-1-1-1-10000002-1-1-12-1-1-1002200-1-10000
χ262222-122222-122-12-12-122-1-1-1-1222-12-1-1-12-1-1-1-1-1-1-1-122-1-1-1-10022002222-2-200000000000-1-1-1-1-1-1000000-2111-211100-2-200110000
χ272222-122222-122-12-12-122-1-1-1-1222-12-1-1-12-1-1-1-1-1-1-1-122-1-1-1-100-2-200-2-2-2-222000000000001111110000002-1-1-12-1-1-100-2-200110000
χ282222-122222-122-12-12-122-1-1-1-1222-12-1-1-12-1-1-1-1-1-1-1-122-1-1-1-100-2-200-2-2-2-2-2-200000000000111111000000-2111-2111002200-1-10000
χ292222-12-2-222-122-12-12-122-1-1-1-12-2-21-2111-2-1-1-1-1-1111-2-21111002-20022-2-22i−2i00000000000-11-1-1110000002i−i−i−i−2iiii002i−2i00−ii0000
χ302222-12-2-222-122-12-12-122-1-1-1-12-2-21-2111-2-1-1-1-1-1111-2-21111002-20022-2-2−2i2i00000000000-11-1-111000000−2iiii2i−i−i−i00−2i2i00i−i0000
χ312222-12-2-222-122-12-12-122-1-1-1-12-2-21-2111-2-1-1-1-1-1111-2-2111100-2200-2-2222i−2i000000000001-111-1-10000002i−i−i−i−2iiii00−2i2i00i−i0000
χ322222-12-2-222-122-12-12-122-1-1-1-12-2-21-2111-2-1-1-1-1-1111-2-2111100-2200-2-222−2i2i000000000001-111-1-1000000−2iiii2i−i−i−i002i−2i00−ii0000
χ33222-12222222-12-1-12-12-1-122-12-1222-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-100002200002222220000000000000-1-1-1-1-1-1-12-1-1-12-1-100002200-1-100
χ34222-12222222-12-1-12-12-1-122-12-1222-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-10000220000-2-222220000000000000-1-1-1-1-1-11-2111-2110000-2-2001100
χ35222-12222222-12-1-12-12-1-122-12-1222-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-10000-2-2000022-2-2-2-20000000000000111111-12-1-1-12-1-10000-2-2001100
χ36222-12222222-12-1-12-12-1-122-12-1222-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-10000-2-20000-2-2-2-2-2-200000000000001111111-2111-21100002200-1-100
χ37222-122-2-2222-12-1-12-12-1-122-12-1-2-2-2111-21-1-1-1-1-11-2-211111100002-200002i−2i22-2-20000000000000-11-1-111−i2i−i−ii−2iii00002i−2i00−ii00
χ38222-122-2-2222-12-1-12-12-1-122-12-1-2-2-2111-21-1-1-1-1-11-2-211111100002-20000−2i2i22-2-20000000000000-11-1-111i−2iii−i2i−i−i0000−2i2i00i−i00
χ39222-122-2-2222-12-1-12-12-1-122-12-1-2-2-2111-21-1-1-1-1-11-2-21111110000-2200002i−2i-2-22200000000000001-111-1-1−i2i−i−ii−2iii0000−2i2i00i−i00
χ40222-122-2-2222-12-1-12-12-1-122-12-1-2-2-2111-21-1-1-1-1-11-2-21111110000-220000−2i2i-2-22200000000000001-111-1-1i−2iii−i2i−i−i00002i−2i00−ii00
χ4122-22222-2-2-2222222-2-2-2-2-2-22222-2-2-2-2-2222-2-2-2222-22-222-2-222000000000000002-2-222-2-2000000000000000000002-20000000000
χ4222-22222-2-2-2222222-2-2-2-2-2-22222-2-2-2-2-2222-2-2-2222-22-222-2-2-2-200000000000000-222-2-22200000000000000000000-220000000000
χ4322-2222-22-2-2222222-2-2-2-2-2-2222-222222-2-22-2-2-22-2-22-22-2-2222200000000000000-22-222-2-200000000000000000000-220000000000
χ4422-2222-22-2-2222222-2-2-2-2-2-2222-222222-2-22-2-2-22-2-22-22-2-222-2-2000000000000002-22-2-222000000000000000000002-20000000000
χ4522-222-12-21122-12-1-1-2-211112-1-1-11-2-2-2-222-1-211-12-11-11-1-111220000−i3i3−i3i300−i3i3−i3i32-2-2-1-11100−i3i3−i3i300−i3i3−i3i300000000-110000000000
χ4622-222-12-21122-12-1-1-2-211112-1-1-11-2-2-2-222-1-211-12-11-11-1-111220000i3−i3i3−i300i3−i3i3−i32-2-2-1-11100i3−i3i3−i300i3−i3i3−i300000000-110000000000
χ4722-222-12-21122-12-1-1-2-211112-1-1-11-2-2-2-222-1-211-12-11-11-1-111-2-20000−i3i3−i3i300i3−i3i3−i3-22211-1-100−i3i3−i3i300i3−i3i3−i3000000001-10000000000
χ4822-222-12-21122-12-1-1-2-211112-1-1-11-2-2-2-222-1-211-12-11-11-1-111-2-20000i3−i3i3−i300−i3i3−i3i3-22211-1-100i3−i3i3−i300−i3i3−i3i3000000001-10000000000
χ4922-222-1-221122-12-1-1-2-211112-1-11-12222-2-2-1-211-1-21-11-111-1-1220000−i3i3i3−i300−i3i3i3−i3-22-2-1-11100−i3i3i3−i300−i3i3i3−i3000000001-10000000000
χ5022-222-1-221122-12-1-1-2-211112-1-11-12222-2-2-1-211-1-21-11-111-1-1220000i3−i3−i3i300i3−i3−i3i3-22-2-1-11100i3−i3−i3i300i3−i3−i3i3000000001-10000000000
χ5122-222-1-221122-12-1-1-2-211112-1-11-12222-2-2-1-211-1-21-11-111-1-1-2-20000−i3i3i3−i300i3−i3−i3i32-2211-1-100−i3i3i3−i300i3−i3−i3i300000000-110000000000
χ5222-222-1-221122-12-1-1-2-211112-1-11-12222-2-2-1-211-1-21-11-111-1-1-2-20000i3−i3−i3i300−i3i3i3−i32-2211-1-100i3−i3−i3i300−i3i3i3−i300000000-110000000000
χ534444-2-244-2-2-24-2-2-214-2-2-211-21-2-2-2-24-2-2-241-2111-211-2-21111004400-2-2-2-20000000000000-2-2111100000000000000000000000000
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χ968-80-48-4004i3−4i3-844-42-400−2i32i34i3−4i344-20000000020−2i32i3-20000000000000000000000000000000000000000000000000000000000000000
χ978-80-4-48000044-82-4-4000000-24400006i−6i002000-200000006i−6i0000000000000000000000000000000000000000000000000000000
χ988-80-4-48000044-82-4-4000000-2440000−6i6i002000-20000000−6i6i0000000000000000000000000000000000000000000000000000000
χ998-80-4-4-400−4i34i3444222002i3−2i32i3−2i3-2-2-200006i−6i00-10−i3i310000033−33−3i3i0000000000000000000000000000000000000000000000000000000
χ1008-80-4-4-400−4i34i3444222002i3−2i32i3−2i3-2-2-20000−6i6i00-10−i3i3100000−33333i−3i0000000000000000000000000000000000000000000000000000000
χ1018-80-4-4-4004i3−4i344422200−2i32i3−2i32i3-2-2-200006i−6i00-10i3−i3100000−3333−3i3i0000000000000000000000000000000000000000000000000000000
χ1028-80-4-4-4004i3−4i344422200−2i32i3−2i32i3-2-2-20000−6i6i00-10i3−i310000033−333i−3i0000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).