Finite Group Databasebeta

← Group #11786267

Character table — Group #11786267

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222288888888888888889999181818181818181818181818181818181818181818187272727272727272
order122244888836661212121224242424242424242222444444444488888888888844444444
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ6111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ7111111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-111
χ8111111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-11111-1-1
χ91-1-11-1111-1-11-1-11-1-1111111-1-1-1-111-1-1-11111-1-1-1-1111-1-11111-1-1-1-1i−ii−ii−ii−i
χ101-1-11-1111-1-11-1-11-1-1111111-1-1-1-111-1-1-11111-1-1-1-1111-1-11111-1-1-1-1−ii−ii−ii−ii
χ111-1-11-1111-1-11-1-11-1-1111111-1-1-1-111-1-1-1-1-1-1-11111111-1-1-1-1-1-11111i−ii−i−ii−ii
χ121-1-11-1111-1-11-1-11-1-1111111-1-1-1-111-1-1-1-1-1-1-11111111-1-1-1-1-1-11111−ii−iii−ii−i
χ131-1-11-11-1-1111-1-11-1-111-1-1-1-1111111-1-1-11111-1-1-1-11-1-111-1-1-1-11111i−i−iii−i−ii
χ141-1-11-11-1-1111-1-11-1-111-1-1-1-1111111-1-1-11111-1-1-1-11-1-111-1-1-1-11111−iii−i−iii−i
χ151-1-11-11-1-1111-1-11-1-111-1-1-1-1111111-1-1-1-1-1-1-111111-1-1111111-1-1-1-1i−i−ii−iii−i
χ161-1-11-11-1-1111-1-11-1-111-1-1-1-1111111-1-1-1-1-1-1-111111-1-1111111-1-1-1-1−iii−ii−i−ii
χ1722222222222222222222222222-2-2-2-2-200000000-2-2-2-2-20000000000000000
χ18222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-200000000-222220000000000000000
χ192222-2-200002222-2-2-2-2000000002222-222-2-222-2-2-200000000000000000000
χ202222-2-200002222-2-2-2-2000000002222-2-2-222-2-222-200000000000000000000
χ212222-2-200002222-2-2-2-200000000-2-2-2-22000000002000022-2-222-2-200000000
χ222222-2-200002222-2-2-2-200000000-2-2-2-220000000020000-2-222-2-22200000000
χ2322-2-200i2−i2i2−i222-2-20000i2i2−i2−i2i2i2−i2−i22-22-20002i−2i002i−2i0i2−i2i2−i22−22−22−22−200000000
χ2422-2-200i2−i2i2−i222-2-20000i2i2−i2−i2i2i2−i2−i22-22-2000−2i2i00−2i2i0i2−i2i2−i2−22−22−22−2200000000
χ2522-2-200i2−i2i2−i222-2-20000i2i2−i2−i2i2i2−i2−i2-22-2202i−2i002i−2i000−i2i2−i2i22−2−222−2−2200000000
χ2622-2-200i2−i2i2−i222-2-20000i2i2−i2−i2i2i2−i2−i2-22-220−2i2i00−2i2i000−i2i2−i2i2−222−2−222−200000000
χ2722-2-200−i2i2−i2i222-2-20000−i2−i2i2i2−i2−i2i2i22-22-20002i−2i002i−2i0−i2i2−i2i2−22−22−22−2200000000
χ2822-2-200−i2i2−i2i222-2-20000−i2−i2i2i2−i2−i2i2i22-22-2000−2i2i00−2i2i0−i2i2−i2i22−22−22−22−200000000
χ2922-2-200−i2i2−i2i222-2-20000−i2−i2i2i2−i2−i2i2i2-22-2202i−2i002i−2i000i2−i2i2−i2−222−2−222−200000000
χ3022-2-200−i2i2−i2i222-2-20000−i2−i2i2i2−i2−i2i2i2-22-220−2i2i00−2i2i000i2−i2i2−i22−2−222−2−2200000000
χ312-22-200i2−i2−i2i22-22-20000i2i2−i2−i2−i2−i2i2i22-2-220002i−2i00−2i2i0i2−i2−i2i22−22−2−22−2200000000
χ322-22-200i2−i2−i2i22-22-20000i2i2−i2−i2−i2−i2i2i22-2-22000−2i2i002i−2i0i2−i2−i2i2−22−222−22−200000000
χ332-22-200i2−i2−i2i22-22-20000i2i2−i2−i2−i2−i2i2i2-222-202i−2i00−2i2i000−i2i2i2−i22−2−22−222−200000000
χ342-22-200i2−i2−i2i22-22-20000i2i2−i2−i2−i2−i2i2i2-222-20−2i2i002i−2i000−i2i2i2−i2−222−22−2−2200000000
χ352-22-200−i2i2i2−i22-22-20000−i2−i2i2i2i2i2−i2−i22-2-220002i−2i00−2i2i0−i2i2i2−i2−22−222−22−200000000
χ362-22-200−i2i2i2−i22-22-20000−i2−i2i2i2i2i2−i2−i22-2-22000−2i2i002i−2i0−i2i2i2−i22−22−2−22−2200000000
χ372-22-200−i2i2i2−i22-22-20000−i2−i2i2i2i2i2−i2−i2-222-202i−2i00−2i2i000i2−i2−i2i2−222−22−2−2200000000
χ382-22-200−i2i2i2−i22-22-20000−i2−i2i2i2i2i2−i2−i2-222-20−2i2i002i−2i000i2−i2−i2i22−2−22−222−200000000
χ392-2-222-200002-2-2222-2-20000000022-2-2222-2-2-2-222-200000000000000000000
χ402-2-222-200002-2-2222-2-20000000022-2-22-2-22222-2-2-200000000000000000000
χ412-2-222-200002-2-2222-2-200000000-2-222-2000000002000022-2-2-2-22200000000
χ422-2-222-200002-2-2222-2-200000000-2-222-20000000020000-2-22222-2-200000000
χ432-2-22-2222-2-22-2-22-2-2222222-2-2-2-2-2-222200000000-2-2-2220000000000000000
χ442-2-22-22-2-2222-2-22-2-222-2-2-2-22222-2-222200000000-222-2-20000000000000000
χ458888888888-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000000000
χ46888888-8-8-8-8-1-1-1-1-1-1-1-1111111110000000000000000000000000000000000
χ478888-8-80000-1-1-1-111113i−3i3i−3i3i−3i3i−3i0000000000000000000000000000000000
χ488888-8-80000-1-1-1-11111−3i3i−3i3i−3i3i−3i3i0000000000000000000000000000000000
χ4988-8-8004i2−4i24i2−4i2-1-1113i−3i3i−3iζ−2ζ3−2ζ+ζ3−ζ+2ζ32ζ−ζ3ζ−2ζ3−2ζ+ζ3−ζ+2ζ32ζ−ζ30000000000000000000000000000000000
χ5088-8-8004i2−4i24i2−4i2-1-111−3i3i−3i3i−2ζ+ζ3ζ−2ζ32ζ−ζ3−ζ+2ζ3−2ζ+ζ3ζ−2ζ32ζ−ζ3−ζ+2ζ30000000000000000000000000000000000
χ5188-8-800−4i24i2−4i24i2-1-1113i−3i3i−3i−ζ+2ζ32ζ−ζ3ζ−2ζ3−2ζ+ζ3−ζ+2ζ32ζ−ζ3ζ−2ζ3−2ζ+ζ30000000000000000000000000000000000
χ5288-8-800−4i24i2−4i24i2-1-111−3i3i−3i3i2ζ−ζ3−ζ+2ζ3−2ζ+ζ3ζ−2ζ32ζ−ζ3−ζ+2ζ3−2ζ+ζ3ζ−2ζ30000000000000000000000000000000000
χ538-88-8004i2−4i2−4i24i2-11-113i−3i−3i3i−2ζ+ζ3ζ−2ζ32ζ−ζ3−ζ+2ζ32ζ−ζ3−ζ+2ζ3−2ζ+ζ3ζ−2ζ30000000000000000000000000000000000
χ548-88-8004i2−4i2−4i24i2-11-11−3i3i3i−3iζ−2ζ3−2ζ+ζ3−ζ+2ζ32ζ−ζ3−ζ+2ζ32ζ−ζ3ζ−2ζ3−2ζ+ζ30000000000000000000000000000000000
χ558-88-800−4i24i24i2−4i2-11-113i−3i−3i3i2ζ−ζ3−ζ+2ζ3−2ζ+ζ3ζ−2ζ3−2ζ+ζ3ζ−2ζ32ζ−ζ3−ζ+2ζ30000000000000000000000000000000000
χ568-88-800−4i24i24i2−4i2-11-11−3i3i3i−3i−ζ+2ζ32ζ−ζ3ζ−2ζ3−2ζ+ζ3ζ−2ζ3−2ζ+ζ3−ζ+2ζ32ζ−ζ30000000000000000000000000000000000
χ578-8-888-80000-111-1-1-1113i−3i3i−3i−3i3i−3i3i0000000000000000000000000000000000
χ588-8-888-80000-111-1-1-111−3i3i−3i3i3i−3i3i−3i0000000000000000000000000000000000
χ598-8-88-8888-8-8-111-111-1-1-1-1-1-111110000000000000000000000000000000000
χ608-8-88-88-8-888-111-111-1-11111-1-1-1-10000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.