Finite Group Databasebeta

← Group #11771150

Character table — Group #11771150

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222244444444444444444444444488881212121212121212121212121212121212121212121212121818181824242424242424242424242436363636363636363636
order12224444444433666666121212121212121212121212121212121212121288888888242424242424242424242424242424242244888824242424242424244444444444
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-1-1-1-111-1-11111-1-1-1-111iiii−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-1-1-1-1-1-111-1-1-1-1111111−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-1-1-1-111-1-11111-1-1-1-111−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-1-1-1-1-1-111-1-1-1-1111111iiii−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−i11-1-1i−ii−iii−i−iii−i−i1-111-1-111-1-1
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−ii−ii−i−iii−i−iii1-1-1-111-1-111
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−iiiii11-1-1i−ii−iii−i−iii−i−i1-1-1-111-1-111
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−ii−ii−i−iii−i−iii1-111-1-111-1-1
χ131111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111i−i−iiii−i−i−i−iii1-1−i−iiiii−i−i
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−iii−i−i−iiiii−i−i1-1ii−i−i−i−iii
χ151111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111i−i−iiii−i−i−i−iii1-1ii−i−i−i−iii
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−iii−i−i−iiiii−i−i1-1−i−iiiii−i−i
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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χ2722-2-2-2-222−2i2i2i−2i2222-2-2-2-2-2-222−2i−2i2i2i-2-2222i2i−2i−2i−2i2i2i−2i0000000000000000000000000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i
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χ374444444444441-21-21-21-211111111-2-2-2-21111-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ384444444444441-21-21-21-211111111-2-2-2-21111-2-2-2-2-2-2-2-2-2-2-2-2111111111111111100000000000000000000000000
χ39444444444444-21-21-21-21-2-2-2-2-2-2-2-21111-2-2-2-2111100000000000000000000000000002222-1-1-1-1-1-1-1-10000000000
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χ4144444444-4-4-4-41-21-21-21-21111-1-1-1-1-2-2-2-2-1-1-1-122222i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii00000000000000000000000000
χ4244444444-4-4-4-41-21-21-21-21111-1-1-1-1-2-2-2-2-1-1-1-12222−2i−2i−2i−2i2i2i2i2iiiiiiiii−i−i−i−i−i−i−i−i00000000000000000000000000
χ4344444444-4-4-4-4-21-21-21-21-2-2-2-2222211112222-1-1-1-1000000000000000000000000000022-2-2-1-1-1-111110000000000
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χ454444-4-4-4-444-4-41-21-21-21-2-1-1-1-111112222-1-1-1-1-2-2222i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii00000000000000000000000000
χ464444-4-4-4-444-4-41-21-21-21-2-1-1-1-111112222-1-1-1-1-2-222−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i00000000000000000000000000
χ474444-4-4-4-444-4-4-21-21-21-212222-2-2-2-2-1-1-1-1222211-1-100000000000000000000000000002i−2i2i−2i−i−iii−i−iii0000000000
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χ494444-4-4-4-4-4-4441-21-21-21-2-1-1-1-1-1-1-1-12222111122-2-222-2-2-2-222-1-1-1-111111111-1-1-1-100000000000000000000000000
χ504444-4-4-4-4-4-4441-21-21-21-2-1-1-1-1-1-1-1-12222111122-2-2-2-22222-2-21111-1-1-1-1-1-1-1-1111100000000000000000000000000
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χ784-4-444i−4i−4i4i00001-2-12-121-2i−i−ii3-3-33−2i2i2i−2i−3i3i3i−3i000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300000000000000000000000000
χ794-4-444i−4i−4i4i00001-2-12-121-2i−i−ii-333-3−2i2i2i−2i3i−3i−3i3i000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300000000000000000000000000
χ804-4-444i−4i−4i4i00001-2-12-121-2i−i−ii-333-3−2i2i2i−2i3i−3i−3i3i000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300000000000000000000000000
χ814-4-444i−4i−4i4i000044-4-4-4-4444i−4i−4i4i00004i−4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ824-4-44−4i4i4i−4i00001-2-12-121-2−iii−i3-3-332i−2i−2i2i3i−3i−3i3i000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300000000000000000000000000
χ834-4-44−4i4i4i−4i00001-2-12-121-2−iii−i3-3-332i−2i−2i2i3i−3i−3i3i000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300000000000000000000000000
χ844-4-44−4i4i4i−4i00001-2-12-121-2−iii−i-333-32i−2i−2i2i−3i3i3i−3i000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300000000000000000000000000
χ854-4-44−4i4i4i−4i00001-2-12-121-2−iii−i-333-32i−2i−2i2i−3i3i3i−3i000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300000000000000000000000000
χ864-4-44−4i4i4i−4i000044-4-4-4-444−4i4i4i−4i0000−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ878-88-88i−8i8i−8i0000-424-2-424-2−4i4i−4i4i00002i−2i2i−2i0000000000000000000000000000000000000000000000000000000000
χ888-88-8−8i8i−8i8i0000-424-2-424-24i−4i4i−4i0000−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000
χ898-8-888i−8i−8i8i0000-424-24-2-42−4i4i4i−4i00002i−2i−2i2i0000000000000000000000000000000000000000000000000000000000
χ908-8-88−8i8i8i−8i0000-424-24-2-424i−4i−4i4i0000−2i2i2i−2i0000000000000000000000000000000000000000000000000000000000

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