Finite Group Databasebeta

← Group #13155328

Character table — Group #13155328

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1122222222222444444444444444444448888888888888899121212121212121212121212121218181818181818242424242424242424242424242424242424242436363636363672727272108108
order1223334466612123336666666612121212121212121236666612121212121212122222888824242424242424242446612126666666624242424242424242424242468888122424242422
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111
χ31111111111111111111111111111111111111111111111111-1-11111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-11-1-1-1-1-1-1
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
χ511111111111111111111111111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-111-1-1-111-1-1-1-1
χ611111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-111-1-1-111-1-1
χ711111111111111111111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-11111
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1-111-1-111
χ9111111-1-1111-1-111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-1i−ii−iii−i−iii−i−i1-1-111-1-111-1-111-1-1iii−i−i−iiii−i−i−i1i−ii−i-1i−ii−i1-1
χ10111111-1-1111-1-111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-1−ii−ii−i−iii−i−iii1-1-111-1-111-1-111-1-1−i−i−iiii−i−i−iiii1−ii−ii-1−ii−ii1-1
χ11111111-1-1111-1-111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-11i−ii−iii−i−iii−i−i1-1-111-1-1-1-111-1-111iii−i−i−iiii−i−i−i1−ii−ii-1−ii−ii-11
χ12111111-1-1111-1-111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-11−ii−ii−i−iii−i−iii1-1-111-1-1-1-111-1-111−i−i−iiii−i−i−iiii1i−ii−i-1i−ii−i-11
χ13111111-1-1111-1-111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1i−i−iiii−i−i−i−iii-111-1-11111-1-111-1-1iii−i−i−i−i−i−iiii-1i−i−ii1i−i−ii-11
χ14111111-1-1111-1-111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1−iii−i−i−iiiii−i−i-111-1-11111-1-111-1-1−i−i−iiiiiii−i−i−i-1−iii−i1−iii−i-11
χ15111111-1-1111-1-111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11i−i−iiii−i−i−i−iii-111-1-111-1-111-1-111iii−i−i−i−i−i−iiii-1−iii−i1−iii−i1-1
χ16111111-1-1111-1-111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11−iii−i−i−iiiii−i−i-111-1-111-1-111-1-111−i−i−iiiiiii−i−i−i-1i−i−ii1i−i−ii1-1
χ1722222-12222-1-1-1-1-1222-122-1-12-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122002222-1-1-1-1-1-1-1-1222-1-1-1-1000000002-1-12-1-12-1-12-1-1-10000-1000000
χ1822222-12222-1-1-1-1-1222-122-1-12-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12200-2-2-2-211111111222-1-1-1-100000000-211-211-211-211-10000-1000000
χ1922222-12222-1-1-1-1-1222-122-1-12-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-20022-2-2-1-1-1-11111-2-2-21111000000002-1-12-1-1-211-211100001000000
χ2022222-12222-1-1-1-1-1222-122-1-12-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-200-2-2221111-1-1-1-1-2-2-2111100000000-211-2112-1-12-1-1100001000000
χ2122222-1-2-222-111-1-1222-122-1-121-2-21111-2-2-1-1-1-1-1-1-2-211111122002i−2i2i−2i−i−iii−i−iii2-2-2-1-111000000002i−i−i−2iii2i−i−i−2iii-100001000000
χ2222222-1-2-222-111-1-1222-122-1-121-2-21111-2-2-1-1-1-1-1-1-2-21111112200−2i2i−2i2iii−i−iii−i−i2-2-2-1-11100000000−2iii2i−i−i−2iii2i−i−i-100001000000
χ2322222-1-2-222-111-1-1222-122-1-121-2-21111-2-2-1-1-1-1-1-1-2-2111111-2-2002i−2i−2i2i−i−iiiii−i−i-22211-1-1000000002i−i−i−2iii−2iii2i−i−i10000-1000000
χ2422222-1-2-222-111-1-1222-122-1-121-2-21111-2-2-1-1-1-1-1-1-2-2111111-2-200−2i2i2i−2iii−i−i−i−iii-22211-1-100000000−2iii2i−i−i2i−i−i−2iii10000-1000000
χ252222-12222-12222-1-12-12-1-12-1-122-122-1-12-1-12-1-1-1-1-1-12-1-1-1-1-1002200220000222200000002-12-1-1-1-1-1000000-1-1-1-1-1-100022000-1-100
χ262222-12222-12222-1-12-12-1-12-1-122-122-1-12-1-12-1-1-1-1-1-12-1-1-1-1-1002200-2-20000-2-2-2-200000002-12-1-1-1-1-1000000111111000-2-20001100
χ272222-12222-12222-1-12-12-1-12-1-122-122-1-12-1-12-1-1-1-1-1-12-1-1-1-1-100-2-20022000022220000000-21-211111000000-1-1-1-1-1-1000-2-20001100
χ282222-12222-12222-1-12-12-1-12-1-122-122-1-12-1-12-1-1-1-1-1-12-1-1-1-1-100-2-200-2-20000-2-2-2-20000000-21-21111100000011111100022000-1-100
χ292222-12-2-22-12-2-22-1-12-12-1-12-1-1-2-21-2-211-21-12-1-1-1-111-211111002-2002i−2i00002i2i−2i−2i00000002-1-21-1-111000000−i−i−iiii0002i−2i000−ii00
χ302222-12-2-22-12-2-22-1-12-12-1-12-1-1-2-21-2-211-21-12-1-1-1-111-211111002-200−2i2i0000−2i−2i2i2i00000002-1-21-1-111000000iii−i−i−i000−2i2i000i−i00
χ312222-12-2-22-12-2-22-1-12-12-1-12-1-1-2-21-2-211-21-12-1-1-1-111-21111100-22002i−2i00002i2i−2i−2i0000000-212-111-1-1000000−i−i−iiii000−2i2i000i−i00
χ322222-12-2-22-12-2-22-1-12-12-1-12-1-1-2-21-2-211-21-12-1-1-1-111-21111100-2200−2i2i0000−2i−2i2i2i0000000-212-111-1-1000000iii−i−i−i0002i−2i000−ii00
χ33222-12222-12222-12-1-122-1-1-12-12-12-1-122-12-1-12-1-1-1-1-1-12-1-1-1-100222200222200000000000-12-12-1-1-1-1-1-1-1-1-1-1000000022000-1-10000
χ34222-12222-12222-12-1-122-1-1-12-12-12-1-122-12-1-12-1-1-1-1-1-12-1-1-1-10022-2-200-2-2-2-200000000000-12-12-1-1-1-11111110000000-2-2000110000
χ35222-12222-12222-12-1-122-1-1-12-12-12-1-122-12-1-12-1-1-1-1-1-12-1-1-1-100-2-222002222000000000001-21-21111-1-1-1-1-1-10000000-2-2000110000
χ36222-12222-12222-12-1-122-1-1-12-12-12-1-122-12-1-12-1-1-1-1-1-12-1-1-1-100-2-2-2-200-2-2-2-2000000000001-21-21111111111000000022000-1-10000
χ37222-122-2-2-122-2-2-12-1-122-1-1-12-1-21-211-2-21-2-1-12-1-1-1111-21111002-22i−2i002i2i−2i−2i00000000000-121-2-1-111−i−i−iiii00000002i−2i000−ii0000
χ38222-122-2-2-122-2-2-12-1-122-1-1-12-1-21-211-2-21-2-1-12-1-1-1111-21111002-2−2i2i00−2i−2i2i2i00000000000-121-2-1-111iii−i−i−i0000000−2i2i000i−i0000
χ39222-122-2-2-122-2-2-12-1-122-1-1-12-1-21-211-2-21-2-1-12-1-1-1111-2111100-222i−2i002i2i−2i−2i000000000001-2-1211-1-1−i−i−iiii0000000−2i2i000i−i0000
χ40222-122-2-2-122-2-2-12-1-122-1-1-12-1-21-211-2-21-2-1-12-1-1-1111-2111100-22−2i2i00−2i−2i2i2i000000000001-2-1211-1-1iii−i−i−i00000002i−2i000−ii0000
χ4122-22222-222222222-2-2-2-2-2222-2222222-2-22-2-2-2-222-2-2-222-2-22200000000000000-22-2222200000000000000000000-20000-2000000
χ4222-22222-222222222-2-2-2-2-2222-2222222-2-22-2-2-2-222-2-2-222-2-2-2-2000000000000002-22-2-2-2-200000000000000000000200002000000
χ4322-2222-22222-2-2222-2-2-2-2-22222-2-2-2-2-2-2222-2-2-2-22-2222-2-2222200000000000000-2-2222-2-200000000000000000000-200002000000
χ4422-2222-22222-2-2222-2-2-2-2-22222-2-2-2-2-2-2222-2-2-2-22-2222-2-222-2-20000000000000022-2-2-2220000000000000000000020000-2000000
χ4522-222-12-222-1-1-1-1-12-2-21-2-2-1-12122-1-1-1-1-2-2-11111-12-211-1-11122000000−i3i3−i3i3−i3i3−i3i3-22-2-1-1-1-1000000000−i3i30−i3i30−i3i30−i3i3100001000000
χ4622-222-12-222-1-1-1-1-12-2-21-2-2-1-12122-1-1-1-1-2-2-11111-12-211-1-11122000000i3−i3i3−i3i3−i3i3−i3-22-2-1-1-1-1000000000i3−i30i3−i30i3−i30i3−i3100001000000
χ4722-222-12-222-1-1-1-1-12-2-21-2-2-1-12122-1-1-1-1-2-2-11111-12-211-1-111-2-2000000−i3i3−i3i3i3−i3i3−i32-221111000000000−i3i30−i3i30i3−i30i3−i3-10000-1000000
χ4822-222-12-222-1-1-1-1-12-2-21-2-2-1-12122-1-1-1-1-2-2-11111-12-211-1-111-2-2000000i3−i3i3−i3−i3i3−i3i32-221111000000000i3−i30i3−i30−i3i30−i3i3-10000-1000000
χ4922-222-1-2222-111-1-12-2-21-2-2-1-12-1-2-2111122-11111-1-22-1-111-1-1220000003−3−333−3−33-2-22-1-1110000000003−30−3303−30−3310000-1000000
χ5022-222-1-2222-111-1-12-2-21-2-2-1-12-1-2-2111122-11111-1-22-1-111-1-122000000−333−3−333−3-2-22-1-111000000000−3303−30−3303−310000-1000000
χ5122-222-1-2222-111-1-12-2-21-2-2-1-12-1-2-2111122-11111-1-22-1-111-1-1-2-20000003−3−33−333−322-211-1-10000000003−30−330−3303−3-100001000000
χ5222-222-1-2222-111-1-12-2-21-2-2-1-12-1-2-2111122-11111-1-22-1-111-1-1-2-2000000−333−33−3−3322-211-1-1000000000−3303−303−30−33-100001000000
χ534444-2-2444-2-2-2-2-21-24-2-2-2-2-21-2-24-2-2-2114-21-21111-2-2-211111000000440000-2-2-2-2000000000000000000000-211-211000000000000
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χ998-80-4-4-40044443−432220006-6-2-2-2000−2323−232300-100-33100003−333−330000000000000000000000000000000000000000000000000000000
χ1008-80-4-4-40044443−43222000-66-2-2-2000−2323−232300-1003-3100003−3−33330000000000000000000000000000000000000000000000000000000
χ1018-80-4-4-400444−43432220006-6-2-2-200023−2323−2300-100-3310000−33−33330000000000000000000000000000000000000000000000000000000
χ1028-80-4-4-400444−4343222000-66-2-2-200023−2323−2300-1003-310000−3333−330000000000000000000000000000000000000000000000000000000

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