Finite Group Databasebeta

← Group #11776147

Character table — Group #11776147

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222244444444444444444444444488881212121212121212121212121212121212121212121212121818181824242424242424242424242436363636363636363636
order1222444444443366666612121212121212121212121212121212121212128888888824242424242424242424242424242424224422446666121212124488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
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
χ511111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11-11-111-1-111-1-111iiii−i−i−i−i
χ611111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-11-11-1-111-1-11111−i−i−i−iiiii
χ711111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11-11-111-1-111-1-111−i−i−i−iiiii
χ811111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-11-11-1-111-1-11111iiii−i−i−i−i
χ91111-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-11-1-1111-1-1-1-1111-1ii−i−iii−i−i
χ101111-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1-111-1-1-11111-1-11-1−i−iii−i−iii
χ111111-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-11-1-1111-1-1-1-1111-1−i−iii−i−iii
χ121111-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1-111-1-1-11111-1-11-1ii−i−iii−i−i
χ131111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-11-111-1-1-1-111
χ141111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111111-1-1-11111-1-1
χ151111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-11111-1-1
χ161111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-111111-111-1-1-1-111
χ172222222222222222222222222222222222222222000000000000000000000000-2-2-2-2000000000000-2-200000000
χ1822222222-2-2-2-2222222222222-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000002222000000000000-2-200000000
χ192222-2-2-2-222-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-2000000000000000000000000-2-222000000000000-2200000000
χ202222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000000000000022-2-2000000000000-2200000000
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χ2222-2-22i2i−2i−2i2i−2i2-2222-2-22-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i22-2-22i−2i2-2000000000000000000000000000000000000000000−22i2−i2i2−i2−22
χ2322-2-22i2i−2i−2i−2i2i-22222-2-22-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i-2-222−2i2i-22000000000000000000000000000000000000000000−i2i2−222−2i2−i2
χ2422-2-22i2i−2i−2i−2i2i-22222-2-22-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i-2-222−2i2i-22000000000000000000000000000000000000000000i2−i22−2−22−i2i2
χ2522-2-2−2i−2i2i2i2i−2i-22222-2-22-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i-2-2222i−2i-22000000000000000000000000000000000000000000−i2i22−2−22i2−i2
χ2622-2-2−2i−2i2i2i2i−2i-22222-2-22-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i-2-2222i−2i-22000000000000000000000000000000000000000000i2−i2−222−2−i2i2
χ2722-2-2−2i−2i2i2i−2i2i2-2222-2-22-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i22-2-2−2i2i2-20000000000000000000000000000000000000000002−2i2−i2i2−i22−2
χ2822-2-2−2i−2i2i2i−2i2i2-2222-2-22-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i22-2-2−2i2i2-2000000000000000000000000000000000000000000−22−i2i2−i2i2−22
χ292-2-222-22-2000022-22-2-2-222-22-200002-22-2000000002−22−22−22−222−2−222−2−222−2−222−2−22-2-220000000000000000000000
χ302-2-222-22-2000022-22-2-2-222-22-200002-22-200000000−i2i2−i2i2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2-222-20000000000000000000000
χ312-2-222-22-2000022-22-2-2-222-22-200002-22-200000000i2−i2i2−i2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-222-20000000000000000000000
χ322-2-222-22-2000022-22-2-2-222-22-200002-22-200000000−22−22−22−22−2−222−2−222−2−222−2−2222-2-220000000000000000000000
χ332-2-22-22-22000022-22-2-2-22-22-220000-22-22000000002−2−22−222−222−2−2−2−222−2−22222−2−2-22-220000000000000000000000
χ342-2-22-22-22000022-22-2-2-22-22-220000-22-2200000000−i2i2i2−i2−i2i2i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i22-22-20000000000000000000000
χ352-2-22-22-22000022-22-2-2-22-22-220000-22-2200000000i2−i2−i2i2i2−i2−i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i22-22-20000000000000000000000
χ362-2-22-22-22000022-22-2-2-22-22-220000-22-2200000000−222−22−2−22−2−22222−2−222−2−2−2−222-22-220000000000000000000000
χ374444444444441-2111-2-2-211111111-2-2-2-21111-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ384444444444441-2111-2-2-211111111-2-2-2-21111-2-2-2-2-2-2-2-2-2-2-2-2111111111111111100000000000000000000000000
χ39444444444444-21-2-2-2111-2-2-2-2-2-2-2-21111-2-2-2-2111100000000000000000000000000002222-1-1-1-1-1-1-1-10000000000
χ40444444444444-21-2-2-2111-2-2-2-2-2-2-2-21111-2-2-2-211110000000000000000000000000000-2-2-2-2111111110000000000
χ4144444444-4-4-4-41-2111-2-2-21111-1-1-1-1-2-2-2-2-1-1-1-122222i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii00000000000000000000000000
χ4244444444-4-4-4-41-2111-2-2-21111-1-1-1-1-2-2-2-2-1-1-1-12222−2i−2i−2i−2i2i2i2i2iiiiiiiii−i−i−i−i−i−i−i−i00000000000000000000000000
χ4344444444-4-4-4-4-21-2-2-2111-2-2-2-2222211112222-1-1-1-100000000000000000000000000002-22-2-1-111-1-1110000000000
χ4444444444-4-4-4-4-21-2-2-2111-2-2-2-2222211112222-1-1-1-10000000000000000000000000000-22-2211-1-111-1-10000000000
χ454444-4-4-4-444-4-41-2111-2-2-2-1-1-1-111112222-1-1-1-1-2-2222i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii00000000000000000000000000
χ464444-4-4-4-444-4-41-2111-2-2-2-1-1-1-111112222-1-1-1-1-2-222−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i00000000000000000000000000
χ474444-4-4-4-444-4-4-21-2-2-21112222-2-2-2-2-1-1-1-1222211-1-100000000000000000000000000002-2-22-1-11111-1-10000000000
χ484444-4-4-4-444-4-4-21-2-2-21112222-2-2-2-2-1-1-1-1222211-1-10000000000000000000000000000-222-211-1-1-1-1110000000000
χ494444-4-4-4-4-4-4441-2111-2-2-2-1-1-1-1-1-1-1-12222111122-2-222-2-2-2-222-1-1-1-111111111-1-1-1-100000000000000000000000000
χ504444-4-4-4-4-4-4441-2111-2-2-2-1-1-1-1-1-1-1-12222111122-2-2-2-22222-2-21111-1-1-1-1-1-1-1-1111100000000000000000000000000
χ514444-4-4-4-4-4-444-21-2-2-211122222222-1-1-1-1-2-2-2-2-1-111000000000000000000000000000022-2-2-1-1-1-111110000000000
χ524444-4-4-4-4-4-444-21-2-2-211122222222-1-1-1-1-2-2-2-2-1-1110000000000000000000000000000-2-2221111-1-1-1-10000000000
χ5344-4-44i4i−4i−4i4i−4i4-41-21-1-1-222ii−i−iii−i−i−2i−2i2i2i11-1-1−2i2i-2200000000−i3i3−i3i33−33−33−33−3−i3i3−i3i300000000000000000000000000
χ5444-4-44i4i−4i−4i4i−4i4-41-21-1-1-222ii−i−iii−i−i−2i−2i2i2i11-1-1−2i2i-2200000000i3−i3i3−i3−33−33−33−33i3−i3i3−i300000000000000000000000000
χ5544-4-44i4i−4i−4i4i−4i4-4-21-2221-1-1−2i−2i2i2i−2i−2i2i2iii−i−i-2-222i−i1-100000000000000000000000000000000−i3i3−i3i33−33−30000000000
χ5644-4-44i4i−4i−4i4i−4i4-4-21-2221-1-1−2i−2i2i2i−2i−2i2i2iii−i−i-2-222i−i1-100000000000000000000000000000000i3−i3i3−i3−33−330000000000
χ5744-4-44i4i−4i−4i−4i4i-441-21-1-1-222ii−i−i−i−iii−2i−2i2i2i-1-1112i−2i2-2000000003−33−3i3−i3i3−i3−i3i3−i3i3−33−3300000000000000000000000000
χ5844-4-44i4i−4i−4i−4i4i-441-21-1-1-222ii−i−i−i−iii−2i−2i2i2i-1-1112i−2i2-200000000−33−33−i3i3−i3i3i3−i3i3−i33−33−300000000000000000000000000
χ5944-4-44i4i−4i−4i−4i4i-44-21-2221-1-1−2i−2i2i2i2i2i−2i−2iii−i−i22-2-2−ii-1100000000000000000000000000000000−i3i3i3−i33−3−330000000000
χ6044-4-44i4i−4i−4i−4i4i-44-21-2221-1-1−2i−2i2i2i2i2i−2i−2iii−i−i22-2-2−ii-1100000000000000000000000000000000i3−i3−i3i3−333−30000000000
χ6144-4-4−4i−4i4i4i4i−4i-441-21-1-1-222−i−iiiii−i−i2i2i−2i−2i-1-111−2i2i2-2000000003−33−3−i3i3−i3i3i3−i3i3−i3−33−3300000000000000000000000000
χ6244-4-4−4i−4i4i4i4i−4i-441-21-1-1-222−i−iiiii−i−i2i2i−2i−2i-1-111−2i2i2-200000000−33−33i3−i3i3−i3−i3i3−i3i33−33−300000000000000000000000000
χ6344-4-4−4i−4i4i4i4i−4i-44-21-2221-1-12i2i−2i−2i−2i−2i2i2i−i−iii22-2-2i−i-1100000000000000000000000000000000−i3i3i3−i3−333−30000000000
χ6444-4-4−4i−4i4i4i4i−4i-44-21-2221-1-12i2i−2i−2i−2i−2i2i2i−i−iii22-2-2i−i-1100000000000000000000000000000000i3−i3−i3i33−3−330000000000
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χ6844-4-4−4i−4i4i4i−4i4i4-4-21-2221-1-12i2i−2i−2i2i2i−2i−2i−i−iii-2-222−ii1-100000000000000000000000000000000i3−i3i3−i33−33−30000000000
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χ814-4-444-44-400001-2-11-122-21-11-1−3i3i3i−3i-22-223i−3i−3i3i0000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ2300000000000000000000000000
χ824-4-444-44-400001-2-11-122-21-11-1−3i3i3i−3i-22-223i−3i−3i3i00002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ2300000000000000000000000000
χ834-4-44-44-4400001-2-11-122-2-11-113i−3i−3i3i2-22-23i−3i−3i3i0000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ2300000000000000000000000000
χ844-4-44-44-4400001-2-11-122-2-11-113i−3i−3i3i2-22-23i−3i−3i3i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ2300000000000000000000000000
χ854-4-44-44-4400001-2-11-122-2-11-11−3i3i3i−3i2-22-2−3i3i3i−3i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ1300000000000000000000000000
χ864-4-44-44-4400001-2-11-122-2-11-11−3i3i3i−3i2-22-2−3i3i3i−3i0000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ1300000000000000000000000000
χ878-88-88i−8i−8i8i0000-4244-4-22-2−4i4i4i−4i00002i−2i−2i2i0000000000000000000000000000000000000000000000000000000000
χ888-88-8−8i8i8i−8i0000-4244-4-22-24i−4i−4i4i0000−2i2i2i−2i0000000000000000000000000000000000000000000000000000000000
χ898-8-888-88-80000-424-44-2-22-44-4400002-22-20000000000000000000000000000000000000000000000000000000000
χ908-8-88-88-880000-424-44-2-224-44-40000-22-220000000000000000000000000000000000000000000000000000000000

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