Finite Group Databasebeta

← Group #11771113

Character table — Group #11771113

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222244444444444444444444444488881212121212121212121212121212121212121212121212121818181824242424242424242424242436363636363636363636
order12224444224433666666666612121212121212121212121266121288888888242424242424242424242424242424242244888824242424242424242488888888
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
χ511111111-1-1-1-1111111-1-1-1-1111111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111-1-11111-1-1-1-111iiii−i−i−i−i
χ611111111-1-1-1-1111111-1-1-1-1111111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-111-1-1-1-1111111−i−i−i−iiiii
χ711111111-1-1-1-1111111-1-1-1-1111111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111-1-11111-1-1-1-111−i−i−i−iiiii
χ811111111-1-1-1-1111111-1-1-1-1111111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-111-1-1-1-1111111iiii−i−i−i−i
χ91111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-111i−ii−iii−i−iii−i−i-1111-1-111-1-1
χ101111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-111−ii−ii−i−iii−i−iii-11-1-111-1-111
χ111111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-111i−ii−iii−i−iii−i−i-11-1-111-1-111
χ121111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-111−ii−ii−i−iii−i−iii-1111-1-111-1-1
χ131111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1i−i−iiii−i−i−i−iii-11−i−iiiii−i−i
χ141111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1−iii−i−i−iiiii−i−i-11ii−i−i−i−iii
χ151111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1i−i−iiii−i−i−i−iii-11ii−i−i−i−iii
χ161111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1−iii−i−i−iiiii−i−i-11−i−iiiii−i−i
χ172222222222222222222222222222222222222222000000000000000000000000-2-2-2-2000000000000-2-200000000
χ1822222222-2-2-2-2222222-2-2-2-2222222-2-22222-2-2-2-2-2-20000000000000000000000002222000000000000-2-200000000
χ192222-2-2-2-222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-200000000000000000000000022-2-20000000000002-200000000
χ202222-2-2-2-2-2-222222222-2-2-2-222-2-2-2-222-2-2-2-222-2-222000000000000000000000000-2-2220000000000002-200000000
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χ2622-2-2−2i−2i2i2i00002222-2-20000-2-2−2i−2i2i2i00−2i−2i2i2i000000−i2i22−2−22i2−i2−i2−i2i2i222−2−2−2−222i2i2−i2−i2-222i−2i0000000000000000000000
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χ292-22-22i−2i2i−2i2-22i−2i22-2-22222-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2-22i−2i0000000000000000000000000000000000000000002−2−i2i22−2−i2i2
χ302-22-22i−2i2i−2i2-22i−2i22-2-22222-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2-22i−2i000000000000000000000000000000000000000000−22i2−i2−22i2−i2
χ312-22-22i−2i2i−2i-22−2i2i22-2-222-2-222-2-22i−2i2i−2i−2i2i2i−2i2i−2i−2i2i-22−2i2i000000000000000000000000000000000000000000−i2i2−22i2−i22−2
χ322-22-22i−2i2i−2i-22−2i2i22-2-222-2-222-2-22i−2i2i−2i−2i2i2i−2i2i−2i−2i2i-22−2i2i000000000000000000000000000000000000000000i2−i22−2−i2i2−22
χ332-22-2−2i2i−2i2i2-2−2i2i22-2-22222-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-2−2i2i0000000000000000000000000000000000000000002−2i2−i22−2i2−i2
χ342-22-2−2i2i−2i2i2-2−2i2i22-2-22222-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-2−2i2i000000000000000000000000000000000000000000−22−i2i2−22−i2i2
χ352-22-2−2i2i−2i2i-222i−2i22-2-222-2-222-2-2−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i-222i−2i000000000000000000000000000000000000000000−i2i22−2i2−i2−22
χ362-22-2−2i2i−2i2i-222i−2i22-2-222-2-222-2-2−2i2i−2i2i2i−2i−2i2i−2i2i2i−2i-222i−2i000000000000000000000000000000000000000000i2−i2−22−i2i22−2
χ374444444444441-21-21-211111-2111111-2-2-2-211-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ384444444444441-21-21-211111-2111111-2-2-2-211-2-2-2-2-2-2-2-2-2-2-2-2111111111111111100000000000000000000000000
χ39444444444444-21-21-21-2-2-2-2-21-2-2-2-2-2-21111-2-2111100000000000000000000000000002222-1-1-1-1-1-1-1-10000000000
χ40444444444444-21-21-21-2-2-2-2-21-2-2-2-2-2-21111-2-211110000000000000000000000000000-2-2-2-2111111110000000000
χ4144444444-4-4-4-41-21-21-2-1-1-1-11-21111-1-1-2-2-2-2-1-122222i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii00000000000000000000000000
χ4244444444-4-4-4-41-21-21-2-1-1-1-11-21111-1-1-2-2-2-2-1-12222−2i−2i−2i−2i2i2i2i2iiiiiiiii−i−i−i−i−i−i−i−i00000000000000000000000000
χ4344444444-4-4-4-4-21-21-212222-21-2-2-2-222111122-1-1-1-1000000000000000000000000000022-2-2-1-1-1-111110000000000
χ4444444444-4-4-4-4-21-21-212222-21-2-2-2-222111122-1-1-1-10000000000000000000000000000-2-2221111-1-1-1-10000000000
χ454444-4-4-4-444-4-41-21-21-211111-2-1-1-1-1-1-12222-1-1-2-2222i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii00000000000000000000000000
χ464444-4-4-4-444-4-41-21-21-211111-2-1-1-1-1-1-12222-1-1-2-222−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i00000000000000000000000000
χ474444-4-4-4-444-4-4-21-21-21-2-2-2-2-21222222-1-1-1-12211-1-100000000000000000000000000002i−2i2i−2i−i−iii−i−iii0000000000
χ484444-4-4-4-444-4-4-21-21-21-2-2-2-2-21222222-1-1-1-12211-1-10000000000000000000000000000−2i2i−2i2iii−i−iii−i−i0000000000
χ494444-4-4-4-4-4-4441-21-21-2-1-1-1-11-2-1-1-1-11122221122-2-222-2-2-2-222-1-1-1-111111111-1-1-1-100000000000000000000000000
χ504444-4-4-4-4-4-4441-21-21-2-1-1-1-11-2-1-1-1-11122221122-2-2-2-22222-2-21111-1-1-1-1-1-1-1-1111100000000000000000000000000
χ514444-4-4-4-4-4-444-21-21-212222-212222-2-2-1-1-1-1-2-2-1-11100000000000000000000000000002i−2i−2i2i−i−iiiii−i−i0000000000
χ524444-4-4-4-4-4-444-21-21-212222-212222-2-2-1-1-1-1-2-2-1-1110000000000000000000000000000−2i2i2i−2iii−i−i−i−iii0000000000
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χ724-44-4−4i4i−4i4i4-4−4i4i-212-1-21-2-2222-12i−2i2i−2i2i−2i−ii−ii2i−2i1-1−ii00000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ734-44-4−4i4i−4i4i-444i−4i1-2-121-2-1-111-12−ii−iii−i2i−2i2i−2ii−i2-2−2i2i00000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ1300000000000000000000000000
χ744-44-4−4i4i−4i4i-444i−4i1-2-121-2-1-111-12−ii−iii−i2i−2i2i−2ii−i2-2−2i2i00000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300000000000000000000000000
χ754-44-4−4i4i−4i4i-444i−4i-212-1-2122-2-22-12i−2i2i−2i−2i2i−ii−ii−2i2i-11i−i00000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ764-44-4−4i4i−4i4i-444i−4i-212-1-2122-2-22-12i−2i2i−2i−2i2i−ii−ii−2i2i-11i−i00000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ774-4-444-4-4400001-2-12-123-3-331-21-1-1133-222-2-3-3000000000000−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i300000000000000000000000000
χ784-4-444-4-4400001-2-12-123-3-331-21-1-1133-222-2-3-3000000000000i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i300000000000000000000000000
χ794-4-444-4-4400001-2-12-12-333-31-21-1-11-3-3-222-2330000000000003−3−33−333−33−3−333−3−3300000000000000000000000000
χ804-4-444-4-4400001-2-12-12-333-31-21-1-11-3-3-222-233000000000000−333−33−3−33−333−3−333−300000000000000000000000000
χ814-4-444-4-44000044-4-4-4-40000444-4-44004-4-4400000000000000000000000000000000000000000000000000000000
χ824-4-44-444-400001-2-12-123-3-331-2-111-1-3-32-2-22330000000000003−3−333−3−33−333−33−3−3300000000000000000000000000
χ834-4-44-444-400001-2-12-123-3-331-2-111-1-3-32-2-2233000000000000−333−3−333−33−3−33−333−300000000000000000000000000
χ844-4-44-444-400001-2-12-12-333-31-2-111-1332-2-22-3-3000000000000−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i300000000000000000000000000
χ854-4-44-444-400001-2-12-12-333-31-2-111-1332-2-22-3-3000000000000i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i300000000000000000000000000
χ864-4-44-444-4000044-4-4-4-4000044-444-400-444-400000000000000000000000000000000000000000000000000000000
χ8788-8-88i8i−8i−8i0000-42-424-200004-2−4i−4i4i4i002i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ8888-8-8−8i−8i8i8i0000-42-424-200004-24i4i−4i−4i00−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ898-8-888-8-880000-424-24-20000-42-444-4002-2-2200000000000000000000000000000000000000000000000000000000
χ908-8-88-888-80000-424-24-20000-424-4-4400-222-200000000000000000000000000000000000000000000000000000000

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