Finite Group Databasebeta

← Group #11785730

Character table — Group #11785730

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122224444444444444444488888888121212121212121218181818181824242424242424242424242424242424242424243672727272
order12222244334666666666612121212661212121212124444444422224488881212121212121212242424242424242448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ5111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1ii−i−i
χ6111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1−i−iii
χ7111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1ii−i−i-1-1-1-11111iiii−i−i−i−i-1−i−iii
χ8111111-1-111-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1−i−iii-1-1-1-11111−i−i−i−iiiii-1ii−i−i
χ91111-1-11111-1111-1-1-1-11111111-1-111-1-1-1-111-1-111-1-111-1-1111-11-111-1-111-1-111-1-111-1-1-11-11-1
χ101111-1-11111-1111-1-1-1-11111111-1-111-1-1-1-111-1-111-1-111-1-111-11-1111-1-111-1-1-1-111-1-111-1-11-11
χ111111-1-11111-1111-1-1-1-11111111-1-111-1-1-1-1-1-111-1-11111-1-1111-11-1-1-111-1-11111-1-111-1-1-1-11-11
χ121111-1-11111-1111-1-1-1-11111111-1-111-1-1-1-1-1-111-1-11111-1-111-11-11-1-111-1-111-1-111-1-111-11-11-1
χ131111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1i−i−ii11-1-1-1-111ii−i−i−i−iii1i−i−ii
χ141111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1−iii−i11-1-1-1-111−i−iiiii−i−i1−iii−i
χ151111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1i−i−ii-1-11111-1-1ii−i−i−i−iii1−iii−i
χ161111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1−iii−i-1-11111-1-1−i−iiiii−i−i1i−i−ii
χ1722222222222222222222222222222222200000000-2-2-2-2-2-200000000000000000000-20000
χ18222222-2-222-22222222222-2-2-2-222-2-2-2-2-2-200000000-2-2-2-2220000000000000000000020000
χ192222-2-22222-2222-2-2-2-22222222-2-222-2-2-2-200000000-2-222-2-20000000000000000000020000
χ202222-2-2-2-2222222-2-2-2-2222-2-2-2-2-2-2-2-2222200000000-2-2222200000000000000000000-20000
χ212-22-2002-2220-2-2-2000022-222-2-2002-20000002i−2i002i−2i2-2002-20000002i−2i002i−2i0000000000000
χ222-22-2002-2220-2-2-2000022-222-2-2002-2000000−2i2i00−2i2i2-2002-2000000−2i2i00−2i2i0000000000000
χ232-22-2002-2220-2-2-2000022-222-2-2002-200002i−2i002i−2i00-2200-2200002i−2i002i−2i000000000000000
χ242-22-2002-2220-2-2-2000022-222-2-2002-20000−2i2i00−2i2i00-2200-220000−2i2i00−2i2i000000000000000
χ252-22-200-22220-2-2-2000022-2-2-22200-220000002i−2i00−2i2i2-200-220000002i−2i00−2i2i0000000000000
χ262-22-200-22220-2-2-2000022-2-2-22200-22000000−2i2i002i−2i2-200-22000000−2i2i002i−2i0000000000000
χ272-22-200-22220-2-2-2000022-2-2-22200-2200002i−2i00−2i2i00-22002-200002i−2i00−2i2i000000000000000
χ282-22-200-22220-2-2-2000022-2-2-22200-220000−2i2i002i−2i00-22002-20000−2i2i002i−2i000000000000000
χ29444444441-2411-2-2-2-2-21-2-2111111-2-211-2-200000000000000222200000000-1-1-1-1-1-1-1-100000
χ30444444441-2411-2-2-2-2-21-2-2111111-2-211-2-200000000000000-2-2-2-2000000001111111100000
χ3144444444-214-2-211111-211-2-2-2-2-2-211-2-211222222220000000000-1-1-1-1-1-1-1-10000000000000
χ3244444444-214-2-211111-211-2-2-2-2-2-211-2-211-2-2-2-2-2-2-2-20000000000111111110000000000000
χ33444444-4-41-2-411-2-2-2-2-21-2-2-1-1-1-11122-1-122000000000000002i2i−2i−2i00000000−i−i−i−iiiii00000
χ34444444-4-41-2-411-2-2-2-2-21-2-2-1-1-1-11122-1-12200000000000000−2i−2i2i2i00000000iiii−i−i−i−i00000
χ35444444-4-4-21-4-2-211111-2112222-2-2-1-122-1-12222-2-2-2-20000000000-1-1-1-111110000000000000
χ36444444-4-4-21-4-2-211111-2112222-2-2-1-122-1-1-2-2-2-2222200000000001111-1-1-1-10000000000000
χ374444-4-4441-2-411-222221-2-21111-1-1-2-2-1-122000000000000002-22-200000000-1-111-1-11100000
χ384444-4-4441-2-411-222221-2-21111-1-1-2-2-1-12200000000000000-22-220000000011-1-111-1-100000
χ394444-4-444-21-4-2-21-1-1-1-1-211-2-2-2-2221122-1-122-2-222-2-20000000000-1-111-1-1110000000000000
χ404444-4-444-21-4-2-21-1-1-1-1-211-2-2-2-2221122-1-1-2-222-2-222000000000011-1-111-1-10000000000000
χ414444-4-4-4-41-2411-222221-2-2-1-1-1-1-1-12211-2-2000000000000002i−2i−2i2i00000000−i−iiiii−i−i00000
χ424444-4-4-4-41-2411-222221-2-2-1-1-1-1-1-12211-2-200000000000000−2i2i2i−2i00000000ii−i−i−i−iii00000
χ434444-4-4-4-4-214-2-21-1-1-1-1-211222222-1-1-2-21122-2-2-2-2220000000000-1-11111-1-10000000000000
χ444444-4-4-4-4-214-2-21-1-1-1-1-211222222-1-1-2-211-2-22222-2-2000000000011-1-1-1-1110000000000000
χ4544-4-400004404-440000-4-4-400000000000000000000004-4000000000000000000000000000
χ4644-4-400004404-440000-4-4-40000000000000000000000-44000000000000000000000000000
χ474-44-4004-4-21022-133-3-3-21-1-2-222001-1003-32i−2i2i−2i2i−2i2i−2i0000000000−ii−ii−ii−ii0000000000000
χ484-44-4004-4-21022-133-3-3-21-1-2-222001-1003-3−2i2i−2i2i−2i2i−2i2i0000000000i−ii−ii−ii−i0000000000000
χ494-44-4004-4-21022-1-3-333-21-1-2-222001-100-332i−2i−2i2i2i−2i−2i2i0000000000−iii−i−iii−i0000000000000
χ504-44-4004-4-21022-1-3-333-21-1-2-222001-100-33−2i2i2i−2i−2i2i2i−2i0000000000i−i−iii−i−ii0000000000000
χ514-44-400-44-21022-133-3-3-21-122-2-200-1100-332i−2i2i−2i−2i2i−2i2i0000000000−ii−iii−ii−i0000000000000
χ524-44-400-44-21022-133-3-3-21-122-2-200-1100-33−2i2i−2i2i2i−2i2i−2i0000000000i−ii−i−ii−ii0000000000000
χ534-44-400-44-21022-1-3-333-21-122-2-200-11003-32i−2i−2i2i−2i2i2i−2i0000000000−iii−ii−i−ii0000000000000
χ544-44-400-44-21022-1-3-333-21-122-2-200-11003-3−2i2i2i−2i2i−2i−2i2i0000000000i−i−ii−iii−i0000000000000
χ554-4-444-4001-20-1122-22-2-12-23i−3i3i−3i1-1003i−3i0000000000000000000000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ2300000
χ564-4-444-4001-20-1122-22-2-12-23i−3i3i−3i1-1003i−3i0000000000000000000000000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ2300000
χ574-4-444-4001-20-1122-22-2-12-2−3i3i−3i3i1-100−3i3i0000000000000000000000000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ1300000
χ584-4-444-4001-20-1122-22-2-12-2−3i3i−3i3i1-100−3i3i0000000000000000000000000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300000
χ594-4-444-400440-44-4-44-44-4-4400004-4000000000000000000000000000000000000000000000
χ604-4-44-44001-20-112-22-22-12-23i−3i3i−3i-1100−3i3i0000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ2300000
χ614-4-44-44001-20-112-22-22-12-23i−3i3i−3i-1100−3i3i0000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ2300000
χ624-4-44-44001-20-112-22-22-12-2−3i3i−3i3i-11003i−3i0000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ1300000
χ634-4-44-44001-20-112-22-22-12-2−3i3i−3i3i-11003i−3i0000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ1300000
χ644-4-44-4400440-44-44-44-4-4-440000-44000000000000000000000000000000000000000000000
χ6588-8-800002-402-2-40000-2446i−6i−6i6i00000000000000000000000000000000000000000000000
χ6688-8-800002-402-2-40000-244−6i6i6i−6i00000000000000000000000000000000000000000000000
χ6788-8-80000-420-4426-6-664-2-2000000000000000000000000000000000000000000000000000
χ6888-8-80000-420-442-666-64-2-2000000000000000000000000000000000000000000000000000
χ698-88-8008-82-40-2-2400002-4422-2-200-440000000000000000000000000000000000000000000
χ708-88-800-882-40-2-2400002-44-2-222004-40000000000000000000000000000000000000000000
χ718-8-888-800-4204-4-2-22-224-220000-44000000000000000000000000000000000000000000000
χ728-8-88-8800-4204-4-22-22-24-2200004-4000000000000000000000000000000000000000000000

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