Finite Group Databasebeta

← Group #11775889

Character table — Group #11775889

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222444444444444488888888881818181818182424242424242424242424242424242436363636363636363648484848
order12222244334666666121212126666121212121212444444224488882424242424242424488888888661212
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ5111111-1-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-11-1ii−i−iiiii−i−i−i−i1iiii−i−i−i−i1-11-1
χ6111111-1-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-11-1−i−iii−i−i−i−iiiii1−i−i−i−iiiii1-11-1
χ7111111-1-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-11-11ii−i−iiiii−i−i−i−i1−i−i−i−iiiii-11-11
χ8111111-1-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-11-11−i−iii−i−i−i−iiiii1iiii−i−i−i−i-11-11
χ91111-1-11111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-111-11-111-1-111-1-1111-1-111-1-11-1-11
χ101111-1-11111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-11-11-11-1-111-1-1111-1-111-1-1111-1-11
χ111111-1-11111-11111111111-1-1-1-111-1-1-1-1-1-1-1-111-111-11-11-111-1-111-1-11-1-111-1-111-111-1
χ121111-1-11111-11111111111-1-1-1-111-1-1-1-1-1-1-1-111-111-1-11-11-1-111-1-111111-1-111-1-1-111-1
χ131111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1i−i−iiii−i−i−i−iii1ii−i−i−i−iii11-1-1
χ141111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1−iii−i−i−iiiii−i−i1−i−iiiii−i−i11-1-1
χ151111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111i−i−iiii−i−i−i−iii1−i−iiiii−i−i-1-111
χ161111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111−iii−i−i−iiiii−i−i1ii−i−i−i−iii-1-111
χ172222222222222222222222222222222-2-2-2-2-2-20000000000000000-2000000000000
χ18222222-2-222-2222222-2-2-2-22222-2-2-2-2-2-222-2-2220000000000000000-2000000000000
χ192222-2-22222-22222222222-2-2-2-222-2-2-2-22222-2-20000000000000000-2000000000000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-22222-2-222220000000000000000-2000000000000
χ212-22-2002i−2i2202-22-2-2-22i2i−2i−2i00002i−2i00002-22i−2i00000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ222-22-2002i−2i2202-22-2-2-22i2i−2i−2i00002i−2i00002-22i−2i0000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ232-22-2002i−2i2202-22-2-2-22i2i−2i−2i00002i−2i0000-22−2i2i00000000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000
χ242-22-2002i−2i2202-22-2-2-22i2i−2i−2i00002i−2i0000-22−2i2i0000000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000
χ252-22-200−2i2i2202-22-2-2-2−2i−2i2i2i0000−2i2i00002-2−2i2i00000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ262-22-200−2i2i2202-22-2-2-2−2i−2i2i2i0000−2i2i00002-2−2i2i0000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ272-22-200−2i2i2202-22-2-2-2−2i−2i2i2i0000−2i2i0000-222i−2i00000000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000
χ282-22-200−2i2i2202-22-2-2-2−2i−2i2i2i0000−2i2i0000-222i−2i0000000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000
χ29444444441-2411-21-2-2111111-2-2-2-211-2-200000000002222-1-1-1-1-1-1-1-10000000000000
χ30444444441-2411-21-2-2111111-2-2-2-211-2-20000000000-2-2-2-2111111110000000000000
χ3144444444-214-2-21-211-2-2-2-2-2-21111-2-2110000002222000000000000000000000-1-1-1-1
χ3244444444-214-2-21-211-2-2-2-2-2-21111-2-211000000-2-2-2-20000000000000000000001111
χ33444444-4-41-2-411-21-2-2-1-1-1-111-2-222-1-12200000000002i2i−2i−2i−i−i−i−iiiii0000000000000
χ34444444-4-41-2-411-21-2-2-1-1-1-111-2-222-1-1220000000000−2i−2i2i2iiiii−i−i−i−i0000000000000
χ35444444-4-4-21-4-2-21-2112222-2-211-1-122-1-10000002-22-2000000000000000000000-11-11
χ36444444-4-4-21-4-2-21-2112222-2-211-1-122-1-1000000-22-220000000000000000000001-11-1
χ374444-4-4441-2-411-21-2-21111-1-122-2-2-1-12200000000002-22-2-1-111-1-1110000000000000
χ384444-4-4441-2-411-21-2-21111-1-122-2-2-1-1220000000000-22-2211-1-111-1-10000000000000
χ394444-4-444-21-4-2-21-211-2-2-2-222-1-11122-1-10000002-2-22000000000000000000000-111-1
χ404444-4-444-21-4-2-21-211-2-2-2-222-1-11122-1-1000000-222-20000000000000000000001-1-11
χ414444-4-4-4-41-2411-21-2-2-1-1-1-1-1-1222211-2-200000000002i−2i−2i2i−i−iiiii−i−i0000000000000
χ424444-4-4-4-41-2411-21-2-2-1-1-1-1-1-1222211-2-20000000000−2i2i2i−2iii−i−i−i−iii0000000000000
χ434444-4-4-4-4-214-2-21-211222222-1-1-1-1-2-21100000022-2-2000000000000000000000-1-111
χ444444-4-4-4-4-214-2-21-211222222-1-1-1-1-2-211000000-2-22200000000000000000000011-1-1
χ4544-4-40000440-4-4-444-40000000000000000004i−4i00000000000000000000000000000
χ4644-4-40000440-4-4-444-4000000000000000000−4i4i00000000000000000000000000000
χ474-4-444-4001-20-112-12-23i−3i3i−3i1-12-2003i−3i0000000000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000000000000
χ484-4-444-4001-20-112-12-23i−3i3i−3i1-12-2003i−3i0000000000000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000000000000
χ494-4-444-4001-20-112-12-2−3i3i−3i3i1-12-200−3i3i0000000000000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000000000
χ504-4-444-4001-20-112-12-2−3i3i−3i3i1-12-200−3i3i0000000000000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000000
χ514-4-444-400440-44-4-4-4400004-4-4400000000000000000000000000000000000000000
χ524-4-44-44001-20-112-12-23i−3i3i−3i-11-2200−3i3i0000000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000000000000
χ534-4-44-44001-20-112-12-23i−3i3i−3i-11-2200−3i3i0000000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ230000000000000
χ544-4-44-44001-20-112-12-2−3i3i−3i3i-11-22003i−3i0000000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000000000
χ554-4-44-44001-20-112-12-2−3i3i−3i3i-11-22003i−3i0000000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000000000000
χ564-4-44-4400440-44-4-4-440000-444-400000000000000000000000000000000000000000
χ5788-8-800002-40-2-242-446-6-66000000000000000000000000000000000000000000000
χ5888-8-800002-40-2-242-44-666-6000000000000000000000000000000000000000000000
χ5988-8-80000-42044-2-42-20000000000006-600000000000000000000000000000000000
χ6088-8-80000-42044-2-42-2000000000000-6600000000000000000000000000000000000
χ618-88-8008i−8i2-402-2-4-2442i2i−2i−2i0000−4i4i000000000000000000000000000000000000000
χ628-88-8008i−8i-420-4424-2-2−4i−4i4i4i00002i−2i000000000000000000000000000000000000000
χ638-88-800−8i8i2-402-2-4-244−2i−2i2i2i00004i−4i000000000000000000000000000000000000000
χ648-88-800−8i8i-420-4424-2-24i4i−4i−4i0000−2i2i000000000000000000000000000000000000000
χ658-8-888-800-4204-4-24-220000-44-2200000000000000000000000000000000000000000
χ668-8-88-8800-4204-4-24-2200004-42-200000000000000000000000000000000000000000

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