Finite Group Databasebeta

← Group #11774041

Character table — Group #11774041

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222444444444444488888888881818181818182424242424242424242424242424242436363636363636363648484848
order122244443346666661212121212121212121212121212224444224488882424242424242424488888888661212
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
χ5111111-1-111-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1ii−i−iiiii−i−i−i−i1iiii−i−i−i−i11-1-1
χ6111111-1-111-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1−i−iii−i−i−i−iiiii1−i−i−i−iiiii11-1-1
χ7111111-1-111-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111ii−i−iiiii−i−i−i−i1−i−i−i−iiiii-1-111
χ8111111-1-111-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111−i−iii−i−i−i−iiiii1iiii−i−i−i−i-1-111
χ91111-1-11111-11111111111-1-111-1-1-1-1-1-111-1-1111-11-11-11-111-1-111-1-1-111-1-111-1-11-11-1
χ101111-1-11111-11111111111-1-111-1-1-1-1-1-111-1-1111-11-1-11-11-1-111-1-111-1-1-111-1-1111-11-1
χ111111-1-11111-11111111111-1-111-1-1-1-1-1-111-1-111-11-111-11-111-1-111-1-1-1-1-111-1-111-11-11
χ121111-1-11111-11111111111-1-111-1-1-1-1-1-111-1-111-11-11-11-11-1-111-1-111-111-1-111-1-1-11-11
χ131111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-11111-1-11-1-11i−i−iiii−i−i−i−iii-1ii−i−i−i−iii1-1-11
χ141111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-11111-1-11-1-11−iii−i−i−iiiii−i−i-1−i−iiiii−i−i1-1-11
χ151111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1i−i−iiii−i−i−i−iii-1−i−iiiii−i−i-111-1
χ161111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1−iii−i−i−iiiii−i−i-1ii−i−i−i−iii-111-1
χ172222222222222222222222222222222-2-2-2-2-2-20000000000000000-2000000000000
χ18222222-2-222-2222222-2-2-2-222-2-2-2-2-2-222-2-222220000000000000000-2000000000000
χ192222-2-22222-22222222222-2-222-2-2-2-2-2-2-2-222-2-200000000000000002000000000000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-22200000000000000002000000000000
χ2122-2-2002i−2i2202-2-22-2-22i−2i2i−2i002i−2i0000002-2002i−2i00000000000000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000
χ2222-2-2002i−2i2202-2-22-2-22i−2i2i−2i002i−2i0000002-2002i−2i0000000000000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000
χ2322-2-2002i−2i2202-2-22-2-22i−2i2i−2i002i−2i000000-2200−2i2i000000000000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000
χ2422-2-2002i−2i2202-2-22-2-22i−2i2i−2i002i−2i000000-2200−2i2i00000000000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000
χ2522-2-200−2i2i2202-2-22-2-2−2i2i−2i2i00−2i2i0000002-200−2i2i0000000000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000
χ2622-2-200−2i2i2202-2-22-2-2−2i2i−2i2i00−2i2i0000002-200−2i2i00000000000000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000
χ2722-2-200−2i2i2202-2-22-2-2−2i2i−2i2i00−2i2i000000-22002i−2i00000000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000
χ2822-2-200−2i2i2202-2-22-2-2−2i2i−2i2i00−2i2i000000-22002i−2i000000000000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000
χ29444444441-24111-2-2-2111111-2-211-2-2-2-200000000002222-1-1-1-1-1-1-1-10000000000000
χ30444444441-24111-2-2-2111111-2-211-2-2-2-20000000000-2-2-2-2111111110000000000000
χ3144444444-214-2-2-2111-2-2-2-2-2-211-2-211110000002222000000000000000000000-1-1-1-1
χ3244444444-214-2-2-2111-2-2-2-2-2-211-2-21111000000-2-2-2-20000000000000000000001111
χ33444444-4-41-2-4111-2-2-2-1-1-1-11122-1-122-2-200000000002i2i−2i−2i−i−i−i−iiiii0000000000000
χ34444444-4-41-2-4111-2-2-2-1-1-1-11122-1-122-2-20000000000−2i−2i2i2iiiii−i−i−i−i0000000000000
χ35444444-4-4-21-4-2-2-21112222-2-2-1-122-1-11100000022-2-2000000000000000000000-1-111
χ36444444-4-4-21-4-2-2-21112222-2-2-1-122-1-111000000-2-22200000000000000000000011-1-1
χ374444-4-4441-2-4111-2-2-21111-1-1-2-2-1-1222200000000002-22-2-1-111-1-1110000000000000
χ384444-4-4441-2-4111-2-2-21111-1-1-2-2-1-122220000000000-22-2211-1-111-1-10000000000000
χ394444-4-444-21-4-2-2-2111-2-2-2-2221122-1-1-1-10000002-22-2000000000000000000000-11-11
χ404444-4-444-21-4-2-2-2111-2-2-2-2221122-1-1-1-1000000-22-220000000000000000000001-11-1
χ414444-4-4-4-41-24111-2-2-2-1-1-1-1-1-12211-2-22200000000002i−2i−2i2i−i−iiiii−i−i0000000000000
χ424444-4-4-4-41-24111-2-2-2-1-1-1-1-1-12211-2-2220000000000−2i2i2i−2iii−i−i−i−iii0000000000000
χ434444-4-4-4-4-214-2-2-2111222222-1-1-2-211-1-10000002-2-22000000000000000000000-111-1
χ444444-4-4-4-4-214-2-2-2111222222-1-1-2-211-1-1000000-222-20000000000000000000001-1-11
χ454-44-40000440-44-4-44-400000000000000004i−4i0000000000000000000000000000000
χ464-44-40000440-44-4-44-40000000000000000−4i4i0000000000000000000000000000000
χ474-4-444-4001-20-1-1122-23i−3i−3i3i1-1003i−3i002-200000000000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000000000
χ484-4-444-4001-20-1-1122-23i−3i−3i3i1-1003i−3i002-200000000000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000000
χ494-4-444-4001-20-1-1122-2−3i3i3i−3i1-100−3i3i002-200000000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000000000000
χ504-4-444-4001-20-1-1122-2−3i3i3i−3i1-100−3i3i002-200000000000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000000000000
χ514-4-444-400440-4-44-4-4400004-4000000-4400000000000000000000000000000000000
χ524-4-44-44001-20-1-1122-23i−3i−3i3i-1100−3i3i00-2200000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000000000
χ534-4-44-44001-20-1-1122-23i−3i−3i3i-1100−3i3i00-2200000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000000000000
χ544-4-44-44001-20-1-1122-2−3i3i3i−3i-11003i−3i00-2200000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000000000000
χ554-4-44-44001-20-1-1122-2−3i3i3i−3i-11003i−3i00-2200000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ230000000000000
χ564-4-44-4400440-4-44-4-440000-440000004-400000000000000000000000000000000000
χ5788-8-8008i−8i2-402-2-2-4442i−2i2i−2i00−4i4i00000000000000000000000000000000000000000
χ5888-8-8008i−8i-420-4442-2-2−4i4i−4i4i002i−2i00000000000000000000000000000000000000000
χ5988-8-800−8i8i2-402-2-2-444−2i2i−2i2i004i−4i00000000000000000000000000000000000000000
χ6088-8-800−8i8i-420-4442-2-24i−4i4i−4i00−2i2i00000000000000000000000000000000000000000
χ618-88-800002-40-22-24-4466-6-6000000000000000000000000000000000000000000000
χ628-88-800002-40-22-24-44-6-666000000000000000000000000000000000000000000000
χ638-88-80000-4204-44-22-200000000006i−6i0000000000000000000000000000000000000
χ648-88-80000-4204-44-22-20000000000−6i6i0000000000000000000000000000000000000
χ658-8-888-800-42044-4-2-220000-44000000-2200000000000000000000000000000000000
χ668-8-88-8800-42044-4-2-2200004-40000002-200000000000000000000000000000000000

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