Finite Group Databasebeta

← Group #11721075

Character table — Group #11721075

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11222466666612121212121818181818183636363636361122246666661212121212181818181818363636363636
order12346123366121236121212882424242444121212122264612666612126612121288242424244412121212
χ11111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1
χ311111111111111111-1-1-1-1-1-11-111-1-111111111111111111-1-1-1-1-1-11-111-1-1
χ411111111111111111-1-1-1-1-1-1-11-1-11111111111111111111-1-1-1-1-1-1-11-1-111
χ52222222-12-122-1-1-1-1-10000000200-1-12222222-12-122-1-1-1-1-10000000200-1-1
χ62222222-12-122-1-1-1-1-10000000-200112222222-12-122-1-1-1-1-10000000-20011
χ7222222-12-12-1-1-1-12-1-122-1-1-1-1000000222222-12-12-1-1-1-12-1-122-1-1-1-1000000
χ8222222-12-12-1-1-1-12-1-1-2-21111000000222222-12-12-1-1-1-12-1-1-2-21111000000
χ9222-22-22222-2-222-2-2-2000000000000222-22-22222-2-222-2-2-2000000000000
χ10222-22-22-12-1-2-2-1-11110000000000−i3i3222-22-22-12-1-2-2-1-11110000000000−i3i3
χ11222-22-22-12-1-2-2-1-11110000000000i3−i3222-22-22-12-1-2-2-1-11110000000000i3−i3
χ12222-22-2-12-1211-1-1-2110033−3−3000000222-22-2-12-1211-1-1-2110033−3−3000000
χ13222-22-2-12-1211-1-1-21100−3−333000000222-22-2-12-1211-1-1-21100−3−333000000
χ142-220-2022-2-2002-20002−22−22−20000002-220-2022-2-2002-20002−22−22−2000000
χ152-220-2022-2-2002-2000−22−22−220000002-220-2022-2-2002-2000−22−22−22000000
χ162-220-20-121-23−3-1103−32−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000002-220-20-121-23−3-1103−32−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ172-220-20-121-23−3-1103−3−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000002-220-20-121-23−3-1103−3−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ182-220-20-121-2−33-110−332−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000002-220-20-121-2−33-110−332−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ192-220-20-121-2−33-110−33−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000002-220-20-121-2−33-110−33−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ20444444-2-2-2-2-2-211-211000000000000444444-2-2-2-2-2-211-211000000000000
χ21444-44-4-2-2-2-222112-1-1000000000000444-44-4-2-2-2-222112-1-1000000000000
χ224-440-404-2-4200-220000000000000004-440-404-2-4200-22000000000000000
χ234-440-40-2-22223−231-10−330000000000004-440-40-2-22223−231-10−33000000000000
χ244-440-40-2-222−23231-103−30000000000004-440-40-2-222−23231-103−3000000000000
χ2566-36-3-30000000000000000020-1-10066-36-3-30000000000000000020-1-100
χ2666-36-3-300000000000000000-20110066-36-3-300000000000000000-201100
χ2766-3-6-330000000000000000000−i3i30066-3-6-330000000000000000000−i3i300
χ2866-3-6-330000000000000000000i3−i30066-3-6-330000000000000000000i3−i300
χ2912-12-60600000000000000000000000012-12-606000000000000000000000000
χ3011111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ3211111111111111111-1-1-1-1-1-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-111
χ3311111111111111111-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-111-1-1
χ342222222-12-122-1-1-1-1-10000000200-1-1-2-2-2-2-2-2-21-21-2-2111110000000-20011
χ352222222-12-122-1-1-1-1-10000000-20011-2-2-2-2-2-2-21-21-2-2111110000000200-1-1
χ36222222-12-12-1-1-1-12-1-122-1-1-1-1000000-2-2-2-2-2-21-21-21111-211-2-21111000000
χ37222222-12-12-1-1-1-12-1-1-2-21111000000-2-2-2-2-2-21-21-21111-21122-1-1-1-1000000
χ38222-22-22222-2-222-2-2-2000000000000-2-2-22-22-2-2-2-222-2-2222000000000000
χ39222-22-22-12-1-2-2-1-11110000000000−i3i3-2-2-22-22-21-212211-1-1-10000000000i3−i3
χ40222-22-22-12-1-2-2-1-11110000000000i3−i3-2-2-22-22-21-212211-1-1-10000000000−i3i3
χ41222-22-2-12-1211-1-1-2110033−3−3000000-2-2-22-221-21-2-1-1112-1-100−3−333000000
χ42222-22-2-12-1211-1-1-21100−3−333000000-2-2-22-221-21-2-1-1112-1-10033−3−3000000
χ432-220-2022-2-2002-20002−22−22−2000000-22-2020-2-22200-22000−22−22−22000000
χ442-220-2022-2-2002-2000−22−22−22000000-22-2020-2-22200-220002−22−22−2000000
χ452-220-20-121-23−3-1103−32−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000-22-20201-2-12−331-10−33−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ462-220-20-121-23−3-1103−3−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000-22-20201-2-12−331-10−332−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ472-220-20-121-2−33-110−332−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000-22-20201-2-123−31-103−3−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ482-220-20-121-2−33-110−33−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000-22-20201-2-123−31-103−32−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ49444444-2-2-2-2-2-211-211000000000000-4-4-4-4-4-4222222-1-12-1-1000000000000
χ50444-44-4-2-2-2-222112-1-1000000000000-4-4-44-442222-2-2-1-1-211000000000000
χ514-440-404-2-4200-22000000000000000-44-4040-424-2002-2000000000000000
χ524-440-40-2-22223−231-10−33000000000000-44-404022-2-2−2323-1103−3000000000000
χ534-440-40-2-222−23231-103−3000000000000-44-404022-2-223−23-110−33000000000000
χ5466-36-3-30000000000000000020-1-100-6-63-63300000000000000000-201100
χ5566-36-3-300000000000000000-201100-6-63-6330000000000000000020-1-100
χ5666-3-6-330000000000000000000−i3i300-6-6363-30000000000000000000i3−i300
χ5766-3-6-330000000000000000000i3−i300-6-6363-30000000000000000000−i3i300
χ5812-12-606000000000000000000000000-121260-6000000000000000000000000

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