Finite Group Databasebeta

← Group #11772760

Character table — Group #11772760

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51
size1124444444444444448888888888242424242424242424242424242448484848487272144144
order12233444666612121212121261212121212121212122488882424242424242424681224242488
χ1111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1
χ31111111111111111111111111111-1-1111111111111-1-1-1-1-111-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111-1-11111-1-1-1-111111-1-11-1-1-1-111ii−i−iiiii−i−i−i−i1-11-1-11-1i−i
χ6111111-1-11111-1-1-1-111111-1-11-1-1-1-111−i−iii−i−i−i−iiiii1-11-1-11-1−ii
χ7111111-1-11111-1-1-1-111111-1-11-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-11-1111-1−ii
χ8111111-1-11111-1-1-1-111111-1-11-1-1-1-1-1-1−i−iii−i−i−i−iiiii-11-1111-1i−i
χ922222222222222222222222222220000000000000000000-2-200
χ10222222-2-22222-2-2-2-222222-2-22-2-2-2-20000000000000000000-2200
χ114441-2444111-21111-2-2-21111-2-2-2-2-2002222-1-1-1-1-1-1-1-1000000000
χ124441-2444111-21111-2-2-21111-2-2-2-2-200-2-2-2-211111111000000000
χ134441-24-4-4111-2-1-1-1-1-2-2-211-1-1-22222002i2i−2i−2i−i−i−i−iiiii000000000
χ144441-24-4-4111-2-1-1-1-1-2-2-211-1-1-2222200−2i−2i2i2iiiii−i−i−i−i000000000
χ154441-2-400111-2333322-2-1-1-3-32000000000033−3−333−3−3000000000
χ164441-2-400111-2333322-2-1-1-3-320000000000−3−333−3−333000000000
χ174441-2-400111-2-3-3-3-322-2-1-13320000000000−i3−i3i3i3i3i3−i3−i3000000000
χ184441-2-400111-2-3-3-3-322-2-1-13320000000000i3i3−i3−i3−i3−i3i3i3000000000
χ1944444-40044440000-4-44-4-400-4000000000000000000000000000
χ20444-21444-2-2-21-2-2-2-2111-2-2-2-21111122000000000000-12-1-1-10000
χ21444-21444-2-2-21-2-2-2-2111-2-2-2-211111-2-20000000000001-21110000
χ22444-214-4-4-2-2-212222111-2-2221-1-1-1-122000000000000-1-2-1110000
χ23444-214-4-4-2-2-212222111-2-2221-1-1-1-1-2-2000000000000121-1-10000
χ2444-4440004-4-44000000-40000000002-200000000000020-2000000
χ2544-4440004-4-44000000-4000000000-22000000000000-202000000
χ2644-4-21000-22212323−23−2333-10000-333−3−32-2000000000000-1013−30000
χ2744-4-21000-22212323−23−2333-10000-333−3−3-2200000000000010-1−330000
χ2844-4-21000-2221−23−23232333-10000-3−3−3332-2000000000000-101−330000
χ2944-4-21000-2221−23−23232333-10000-3−3−333-2200000000000010-13−30000
χ304-401-202i−2i-13-32−ζ2−2ζ7+ζ10−2ζ11ζ2+2ζ7−ζ10+2ζ11−ζ2+2ζ7+ζ10+2ζ11ζ2−2ζ7−ζ10−2ζ1123−2303−3i−i0−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11001+i−1−i1−i−1+iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7−ζ2−ζ7ζ2+ζ7ζ10+ζ11−ζ10−ζ11000000000
χ314-401-202i−2i-13-32−ζ2−2ζ7+ζ10−2ζ11ζ2+2ζ7−ζ10+2ζ11−ζ2+2ζ7+ζ10+2ζ11ζ2−2ζ7−ζ10−2ζ1123−2303−3i−i0−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100−1−i1+i−1+i1−i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7ζ2+ζ7−ζ2−ζ7−ζ10−ζ11ζ10+ζ11000000000
χ324-401-202i−2i-13-32ζ2−2ζ7−ζ10−2ζ11−ζ2+2ζ7+ζ10+2ζ11ζ2+2ζ7−ζ10+2ζ11−ζ2−2ζ7+ζ10−2ζ11−23230−33i−i0ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11001+i−1−i1−i−1+iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11−ζ10−ζ11ζ10+ζ11ζ2+ζ7−ζ2−ζ7000000000
χ334-401-202i−2i-13-32ζ2−2ζ7−ζ10−2ζ11−ζ2+2ζ7+ζ10+2ζ11ζ2+2ζ7−ζ10+2ζ11−ζ2−2ζ7+ζ10−2ζ11−23230−33i−i0ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100−1−i1+i−1+i1−i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11ζ10+ζ11−ζ10−ζ11−ζ2−ζ7ζ2+ζ7000000000
χ344-401-20−2i2i-13-32−ζ2+2ζ7+ζ10+2ζ11ζ2−2ζ7−ζ10−2ζ11−ζ2−2ζ7+ζ10−2ζ11ζ2+2ζ7−ζ10+2ζ11−23230−33−ii0−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11001−i−1+i1+i−1−iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7−ζ2+ζ7ζ2−ζ7ζ10−ζ11−ζ10+ζ11000000000
χ354-401-20−2i2i-13-32−ζ2+2ζ7+ζ10+2ζ11ζ2−2ζ7−ζ10−2ζ11−ζ2−2ζ7+ζ10−2ζ11ζ2+2ζ7−ζ10+2ζ11−23230−33−ii0−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100−1+i1−i−1−i1+i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7ζ2−ζ7−ζ2+ζ7−ζ10+ζ11ζ10−ζ11000000000
χ364-401-20−2i2i-13-32ζ2+2ζ7−ζ10+2ζ11−ζ2−2ζ7+ζ10−2ζ11ζ2−2ζ7−ζ10−2ζ11−ζ2+2ζ7+ζ10+2ζ1123−2303−3−ii0ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11001−i−1+i1+i−1−iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11−ζ10+ζ11ζ10−ζ11ζ2−ζ7−ζ2+ζ7000000000
χ374-401-20−2i2i-13-32ζ2+2ζ7−ζ10+2ζ11−ζ2−2ζ7+ζ10−2ζ11ζ2−2ζ7−ζ10−2ζ11−ζ2+2ζ7+ζ10+2ζ1123−2303−3−ii0ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100−1+i1−i−1−i1+i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11ζ10−ζ11−ζ10+ζ11−ζ2+ζ7ζ2−ζ7000000000
χ384-404402i−2i-400-42i−2i−2i2i00000−2i2i0−2i2i2i−2i001+i−1−i1−i−1+i−1−i1+i−1−i1+i1−i−1+i−1+i1−i000000000
χ394-404402i−2i-400-42i−2i−2i2i00000−2i2i0−2i2i2i−2i00−1−i1+i−1+i1−i1+i−1−i1+i−1−i−1+i1−i1−i−1+i000000000
χ404-40440−2i2i-400-4−2i2i2i−2i000002i−2i02i−2i−2i2i001−i−1+i1+i−1−i−1+i1−i−1+i1−i1+i−1−i−1−i1+i000000000
χ414-40440−2i2i-400-4−2i2i2i−2i000002i−2i02i−2i−2i2i00−1+i1−i−1−i1+i1−i−1+i1−i−1+i−1−i1+i1+i−1−i000000000
χ42888-42-800-4-4-420000-2-224400-2000000000000000000000000000
χ4388-82-40002-2-2-42323−23−2300400000−23−23232300000000000000000000000
χ4488-82-40002-2-2-4−23−232323004000002323−23−2300000000000000000000000
χ4588-8-42000-44420000-6-6-200006000000000000000000000000000
χ468-802-404i−4i-2-664−2i2i2i−2i00000−4i4i02i−2i−2i2i00000000000000000000000
χ478-802-40−4i4i-2-6642i−2i−2i2i000004i−4i0−2i2i2i−2i00000000000000000000000
χ488-80-4204i−4i400-2−2ζ2+2ζ7+2ζ10+2ζ112ζ2−2ζ7−2ζ10−2ζ11−2ζ2−2ζ7+2ζ10−2ζ112ζ2+2ζ7−2ζ10+2ζ11−2323023−232i−2i0ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000000
χ498-80-4204i−4i400-22ζ2+2ζ7−2ζ10+2ζ11−2ζ2−2ζ7+2ζ10−2ζ112ζ2−2ζ7−2ζ10−2ζ11−2ζ2+2ζ7+2ζ10+2ζ1123−230−23232i−2i0−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000000
χ508-80-420−4i4i400-2−2ζ2−2ζ7+2ζ10−2ζ112ζ2+2ζ7−2ζ10+2ζ11−2ζ2+2ζ7+2ζ10+2ζ112ζ2−2ζ7−2ζ10−2ζ1123−230−2323−2i2i0ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000000
χ518-80-420−4i4i400-22ζ2−2ζ7−2ζ10−2ζ11−2ζ2+2ζ7+2ζ10+2ζ112ζ2+2ζ7−2ζ10+2ζ11−2ζ2−2ζ7+2ζ10−2ζ11−2323023−23−2i2i0−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.