Finite Group Databasebeta

← Group #13049447

Character table — Group #13049447

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size112222444444444488888888888888181818363636363636363636363636545454545454108108108
order12336633333666663333333666666641212266666666121212882424242441212
χ1111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1111111111-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111
χ5222222222222222222222222222222-2-2-2000000000-2-2-2000000000
χ6222-12-12-12-1-12-1-1-1222-1-1-1-1-122-1-1-1-1-12222-1-122-1-1-1-1-1-1-1000000000
χ7222-12-12-12-1-12-1-1-1222-1-1-1-1-122-1-1-1-1-1222-211-2-21111-1-1-1000000000
χ8222-12-12-12-1-12-1-1-1222-1-1-1-1-122-1-1-1-1-1-2-2-20−i3i300−i3−i3i3i3111000000000
χ9222-12-12-12-1-12-1-1-1222-1-1-1-1-122-1-1-1-1-1-2-2-20i3−i300i3i3−i3−i3111000000000
χ1022-12-122-1222222-12-1-12-1-1-1-1-1-12-1-1-1-12-1-10000000002-1-122-1-1-1-1000
χ1122-12-122-1222222-12-1-12-1-1-1-1-1-12-1-1-1-12-1-10000000002-1-1-2-21111000
χ1222-12-122-1222222-12-1-12-1-1-1-1-1-12-1-1-1-1-211000000000-2110033−3−3000
χ1322-12-122-1222222-12-1-12-1-1-1-1-1-12-1-1-1-1-211000000000-21100−3−333000
χ142-222-2-222222-2-2-2-2-22222222-2-2-2-2-2-2-2000000000000000−i2i2−i2i2−i2i2000
χ152-222-2-222222-2-2-2-2-22222222-2-2-2-2-2-2-2000000000000000i2−i2i2−i2i2−i2000
χ162-2-121-22-1222-2-2-21-2-1-12-1-1-1-111-2111103−300000000003−3−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000
χ172-2-121-22-1222-2-2-21-2-1-12-1-1-1-111-2111103−300000000003−3i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000
χ182-2-121-22-1222-2-2-21-2-1-12-1-1-1-111-211110−330000000000−33−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000
χ192-2-121-22-1222-2-2-21-2-1-12-1-1-1-111-211110−330000000000−33i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000
χ2044444414-2-2-2-2-2-2411-2111-2-21-2111-2-20000000000000000000002-1-1
χ2144444414-2-2-2-2-2-2411-2111-2-21-2111-2-2000000000000000000000-211
χ22444444-241111114-2-21-2-2-211-21-2-2-211000222-1-1-1-1-1-1000000000000
χ23444444-241111114-2-21-2-2-211-21-2-2-211000-2-2-2111111000000000000
χ24444-24-2-2-21−1−3i32−1+3i321−1−3i32−1+3i32-2-2-21111−1−3i32−1+3i32-21111−1−3i32−1+3i320002−1−i3−1+i3-1-11+i321+i321−i321−i32000000000000
χ25444-24-2-2-21−1−3i32−1+3i321−1−3i32−1+3i32-2-2-21111−1−3i32−1+3i32-21111−1−3i32−1+3i32000-21+i31−i311−1−i32−1−i32−1+i32−1+i32000000000000
χ26444-24-2-2-21−1+3i32−1−3i321−1+3i32−1−3i32-2-2-21111−1+3i32−1−3i32-21111−1+3i32−1−3i320002−1+i3−1−i3-1-11−i321−i321+i321+i32000000000000
χ27444-24-2-2-21−1+3i32−1−3i321−1+3i32−1−3i32-2-2-21111−1+3i32−1−3i32-21111−1+3i32−1−3i32000-21−i31+i311−1+i32−1+i32−1−i32−1−i32000000000000
χ2844-2-2-2-2414-2-24-2-214-2-2-21111-2-2-211114-2-2000000000-211000000000
χ2944-2-2-2-2414-2-24-2-214-2-2-21111-2-2-21111-4220000000002-1-1000000000
χ304-444-4-414-2-2-2222-4-11-2111-2-2-12-1-1-12200000000000000000000003−3
χ314-444-4-414-2-2-2222-4-11-2111-2-2-12-1-1-1220000000000000000000000−33
χ324-444-4-4-24111-1-1-1-42-21-2-2-2112-1222-1-1000000−i3i3−i3i3−i3i3000000000000
χ334-444-4-4-24111-1-1-1-42-21-2-2-2112-1222-1-1000000i3−i3i3−i3i3−i3000000000000
χ344-44-2-424-24-2-2-4222-444-2-2-2-2-2-4-422222000000000000000000000000
χ354-44-2-42-2-21−1−3i32−1+3i32-11+3i321−3i3222-21111−1−3i32−1+3i322-1-1-1-11+3i321−3i32000000−i3i3−3+i323−i323+i32−3−i32000000000000
χ364-44-2-42-2-21−1−3i32−1+3i32-11+3i321−3i3222-21111−1−3i32−1+3i322-1-1-1-11+3i321−3i32000000i3−i33−i32−3+i32−3−i323+i32000000000000
χ374-44-2-42-2-21−1+3i32−1−3i32-11−3i321+3i3222-21111−1+3i32−1−3i322-1-1-1-11−3i321+3i32000000−i3i33+i32−3−i32−3+i323−i32000000000000
χ384-44-2-42-2-21−1+3i32−1−3i32-11−3i321+3i3222-21111−1+3i32−1−3i322-1-1-1-11−3i321+3i32000000i3−i3−3−i323+i323−i32−3+i32000000000000
χ394-4-2-222414-2-2-422-1-4-2-2-21111222-1-1-1-1023−230000000000−33000000000
χ404-4-2-222414-2-2-422-1-4-2-2-21111222-1-1-1-10−232300000000003−3000000000
χ41888-48-42-4-422-422-422-4-1-1-1222-4-1-1-122000000000000000000000000
χ4288-48-482-4-4-4-4-4-4-4-42-122-1-122-122-1-122000000000000000000000000
χ4388-48-48-4-4222222-4-42-1-422-1-12-1-422-1-1000000000000000000000000
χ4488-4-4-4-422-422-42222-12-15-4-1-1-12-15-4-1-1000000000000000000000000
χ4588-4-4-4-422-422-42222-12-1-45-1-1-12-1-45-1-1000000000000000000000000
χ4688-4-4-4-4-422−1−3i3−1+3i32−1−3i3−1+3i32-42-12-1-11+3i321−3i322-12-1-11+3i321−3i32000000000000000000000000
χ4788-4-4-4-4-422−1+3i3−1−3i32−1+3i3−1−3i32-42-12-1-11−3i321+3i322-12-1-11−3i321+3i32000000000000000000000000
χ488-88-4-842-4-4224-2-24-22-4-1-1-122-24111-2-2000000000000000000000000
χ498-8-484-82-4-4-4-44444-2-122-1-1221-2-211-2-2000000000000000000000000
χ508-8-484-8-4-4222-2-2-2442-1-422-1-1-214-2-211000000000000000000000000
χ518-8-4-44422-4224-2-2-2-2-12-15-4-1-11-21-5411000000000000000000000000
χ528-8-4-44422-4224-2-2-2-2-12-1-45-1-11-214-511000000000000000000000000
χ538-8-4-444-422−1−3i3−1+3i3-21+3i31−3i3-242-12-1-11+3i321−3i32-21-211−1−3i32−1+3i32000000000000000000000000
χ548-8-4-444-422−1+3i3−1−3i3-21−3i31+3i3-242-12-1-11−3i321+3i32-21-211−1+3i32−1−3i32000000000000000000000000

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