Finite Group Databasebeta

← Group #11787414

Character table — Group #11787414

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222244444444444444444444444488881212121212121212121212121212121212121212121212121818181824242424242424242424242436363636363636363636
order12224444888833666666121212121212121224242424242424242424242422446666888812121212242424242424242422442466881212242424244444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ511111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11111
χ611111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1
χ711111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1
χ811111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-11111-1-1-1-1-1-11111
χ91111-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i11-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i-1-1111-111i−i-1-1ii−i−iii−i−ii−i11-1-1
χ101111-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i11-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i-1-111-11-1-1−ii11−i−iii−i−iiii−i-1-111
χ111111-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i-1-111-1-1-1-1−i−iii1111−i−i−i−iiiii-1-1111-111i−i-1-1ii−i−i−i−iiii−i-1-111
χ121111-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i-1-111-1-1-1-1−i−iii1111−i−i−i−iiiii-1-111-11-1-1−ii11−i−iiiii−i−ii−i11-1-1
χ131111-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii11-1-11111−i−iii-1-1-1-1−i−i−i−iiiii-1-1111-111−ii-1-1−i−iii−i−iii−ii11-1-1
χ141111-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii11-1-11111−i−iii-1-1-1-1−i−i−i−iiiii-1-111-11-1-1i−i11ii−i−iii−i−i−ii-1-111
χ151111-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−i-1-1111-111−ii-1-1−i−iiiii−i−i−ii-1-111
χ161111-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−i-1-111-11-1-1i−i11ii−i−i−i−iii−ii11-1-1
χ172222222222222222222222222222222222222222000000000000000000000000-2-2-2-20000000000000000-2-20000
χ1822222222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000-2-2-2-20000000000000000220000
χ192222-2-2-2-22i2i−2i−2i22222222-2-2-2-2-2-2-2-22i2i2i2i−2i−2i−2i−2i2i2i−2i−2i00000000000000000000000022-2-20000000000000000−2i2i0000
χ202222-2-2-2-2−2i−2i2i2i22222222-2-2-2-2-2-2-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i00000000000000000000000022-2-200000000000000002i−2i0000
χ2122-2-22i−2i2i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132222-2-2-2-22i−2i2i−2i2i−2i2i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000000000000000001+i−1−i1−i−1+i002−2−i2i2
χ2222-2-22i−2i2i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132222-2-2-2-22i−2i2i−2i2i−2i2i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000000000000000−1−i1+i−1+i1−i00−22i2−i2
χ2322-2-22i−2i2i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132222-2-2-2-22i−2i2i−2i2i−2i2i−2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000000000000000001+i−1−i1−i−1+i00−22i2−i2
χ2422-2-22i−2i2i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132222-2-2-2-22i−2i2i−2i2i−2i2i−2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000000000000000000000−1−i1+i−1+i1−i002−2−i2i2
χ2522-2-2−2i2i−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232222-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000000000001−i−1+i1+i−1−i002−2i2−i2
χ2622-2-2−2i2i−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232222-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000000000000000000000−1+i1−i−1−i1+i00−22−i2i2
χ2722-2-2−2i2i−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232222-2-2-2-2−2i2i−2i2i−2i2i−2i2i2ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000000000000000001−i−1+i1+i−1−i00−22−i2i2
χ2822-2-2−2i2i−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232222-2-2-2-2−2i2i−2i2i−2i2i−2i2i2ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000000000000000000000000000−1+i1−i−1−i1+i002−2i2−i2
χ292-2-2222-2-2000022-2-2-2-22222-2-222-2-2000000000000000000002i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i2-22-20000000000000000000000
χ302-2-2222-2-2000022-2-2-2-22222-2-222-2-200000000000000000000−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i2-22-20000000000000000000000
χ312-2-2222-2-2000022-2-2-2-22222-2-222-2-20000000000002-22-222-2-2000022-2-200000000-22-220000000000000000000000
χ322-2-2222-2-2000022-2-2-2-22222-2-222-2-2000000000000-22-22-2-2220000-2-22200000000-22-220000000000000000000000
χ332-2-22-2-222000022-2-2-2-222-2-222-2-222000000000000000000002-2-22000022-2-2-2-222-222-20000000000000000000000
χ342-2-22-2-222000022-2-2-2-222-2-222-2-22200000000000000000000-222-20000-2-22222-2-2-222-20000000000000000000000
χ352-2-22-2-222000022-2-2-2-222-2-222-2-2220000000000002-2-2222-2-20000-2-222000000002-2-220000000000000000000000
χ362-2-22-2-222000022-2-2-2-222-2-222-2-222000000000000-222-2-2-222000022-2-2000000002-2-220000000000000000000000
χ374444444444441-21-21-21-211-2-2-2-21111111111-2-2-2-22222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ384444444444441-21-21-21-211-2-2-2-21111111111-2-2-2-2-2-2-2-21111-2-2-2-211111111111100000000000000000000000000
χ39444444444444-21-21-21-21-2-21111-2-2-2-2-2-2-2-2-2-21111000000000000000000000000000022-1-122-1-1-1-1-1-10000000000
χ40444444444444-21-21-21-21-2-21111-2-2-2-2-2-2-2-2-2-211110000000000000000000000000000-2-211-2-21111110000000000
χ4144444444-4-4-4-41-21-21-21-211-2-2-2-211-1-1-1-1-1-1-1-122222222-1-1-1-1-2-2-2-2-1-1-1-11111111100000000000000000000000000
χ4244444444-4-4-4-41-21-21-21-211-2-2-2-211-1-1-1-1-1-1-1-12222-2-2-2-2111122221111-1-1-1-1-1-1-1-100000000000000000000000000
χ4344444444-4-4-4-4-21-21-21-21-2-21111-2-222222222-1-1-1-1000000000000000000000000000022-1-1-2-2-1-111110000000000
χ4444444444-4-4-4-4-21-21-21-21-2-21111-2-222222222-1-1-1-10000000000000000000000000000-2-2112211-1-1-1-10000000000
χ454444-4-4-4-44i4i−4i−4i1-21-21-21-2-1-12222-1-1iiii−i−i−i−i−2i−2i2i2i22-2-2-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii00000000000000000000000000
χ464444-4-4-4-44i4i−4i−4i1-21-21-21-2-1-12222-1-1iiii−i−i−i−i−2i−2i2i2i-2-2221111−2i−2i2i2i-1-1-1-1iiii−i−i−i−i00000000000000000000000000
χ474444-4-4-4-44i4i−4i−4i-21-21-21-2122-1-1-1-122−2i−2i−2i−2i2i2i2i2iii−i−i00000000000000000000000000002-2-1-12i−2i11−i−iii0000000000
χ484444-4-4-4-44i4i−4i−4i-21-21-21-2122-1-1-1-122−2i−2i−2i−2i2i2i2i2iii−i−i0000000000000000000000000000-2211−2i2i-1-1ii−i−i0000000000
χ494444-4-4-4-4−4i−4i4i4i1-21-21-21-2-1-12222-1-1−i−i−i−iiiii2i2i−2i−2i22-2-2-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−i00000000000000000000000000
χ504444-4-4-4-4−4i−4i4i4i1-21-21-21-2-1-12222-1-1−i−i−i−iiiii2i2i−2i−2i-2-22211112i2i−2i−2i-1-1-1-1−i−i−i−iiiii00000000000000000000000000
χ514444-4-4-4-4−4i−4i4i4i-21-21-21-2122-1-1-1-1222i2i2i2i−2i−2i−2i−2i−i−iii00000000000000000000000000002-2-1-1−2i2i11ii−i−i0000000000
χ524444-4-4-4-4−4i−4i4i4i-21-21-21-2122-1-1-1-1222i2i2i2i−2i−2i−2i−2i−i−iii0000000000000000000000000000-22112i−2i-1-1−i−iii0000000000
χ5344-4-44i−4i4i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ131-21-2-12-12i−i−2i2i−2i2ii−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−i3i3−i3i300003−33−3−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ1300000000000000000000000000
χ5444-4-44i−4i4i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ131-21-2-12-12i−i−2i2i−2i2ii−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000i3−i3i3−i30000−33−33ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300000000000000000000000000
χ5544-4-44i−4i4i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ13-21-212-12-1−2i2ii−ii−i−2i2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13000000000000000000000000000000−i3i3003−3−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ5644-4-44i−4i4i−4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ13-21-212-12-1−2i2ii−ii−i−2i2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13000000000000000000000000000000i3−i300−33ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ5744-4-44i−4i4i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ131-21-2-12-12i−i−2i2i−2i2ii−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−i3i3−i3i300003−33−3ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300000000000000000000000000
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χ6244-4-4−4i4i−4i4i−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ231-21-2-12-12−ii2i−2i2i−2i−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000i3−i3i3−i300003−33−3ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300000000000000000000000000
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χ878-88-88i−8i−8i8i0000-424-2-424-2−4i4i−2i2i2i−2i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ888-88-8−8i8i8i−8i0000-424-2-424-24i−4i2i−2i−2i2i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ898-8-8888-8-80000-424-24-2-42-4-4-2-2224400000000000000000000000000000000000000000000000000000000000000
χ908-8-88-8-8880000-424-24-2-424422-2-2-4-400000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.